Answer:
the answers d
A Carnot heat engine and an irreversible heat engine both operate between the same high-temperature and low-temperature reservoirs. They absorb the same energy from the high-temperature reservoir as heat. The irreversible engine cannot absorb the same energy from the high-temperature reservoir as heat without violating the second law of thermodynamics, therefore the correct option is E.
What is a Carnot engine?It is a theoretical engine assumed to have the maximum efficiency among all engines out there in the universe.
No other engine can have greater efficiency than the Carnot engine.
The Carnot engine work on the principle of the Carnot cycle which assume that the heat and work tranfer processes are reversible in nature. there is no loss due to the friction of the piston.
As we know from the second law of thermodynamics that no other engine can have greater efficiency than the Carnot engine.
Thus, the irreversible engine cannot absorb the same energy from the high-temperature reservoir as heat without violating the second law of thermodynamics, therefore the correct option is E.
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A 2MeV proton is moving perpendicular to a uniform magnetic field of 2.5 T.the force on a proton is
Answer:
7.8x10-12N
Explanation:
We know that
Magnetic force = F = qVB
And
Also Kinetic energy K.E is
E = (1/2)mV²
So making v subject
V = √(2E / m)
And
E = KE = 2MeV
= 2 × 106 eV
= 2 × 106 × 1.6 × 10–19 J
= 3.2 × 10–13 J
And then
V= √2x3.2E-13/1.6E-27
1.9E7m/s
Given that
mass of proton = 1.6 × 10–27 kg,
Magnetic field strength B = 2.5 T.
So F= qBv sinစ
=
So F = 1.6 × 10–19 × 2.5 × 1.9 x10^7 x sin 90°
= 7.8 x 10^-12N
Answer:
8*10^-12
Explanation:
Given that
Energy of proton, K = 2 MeV = 2 * 1.6*10^-19 *10^6 = 3.2*10^-13
magnetic field strength, B = 2.5 T
mass of proton, m = 1.67*10^-27 kg
K = ½mv², making v² the subject of formula by rearranging, we have
v² = 2k/m
v² = (2 * 3.2*10^-13) / 1.67*10^-27
v² = 6.4*10^-13 / 1.6*10^-27
v² = 4*10^14
v = √4*10^14
v = 2*10^7 m/s
f = qvbsinθ, where
θ = 90
v = 2*10^7 m/s
b = 2.5 T
q = 1.6*10^-19
f = 1.6*10^-19 * 2*10^7 * 2.5 sin 90
f = 8*10^-12 N
thus, the force on the proton is 8*10^-12
A nucleus of carbon 14 has 6 protons and 8 neutrons. The atomic number and mass number of carbon 14 are, respectively,
a) 6 and 8
b) 6 and 14
c) 8 and 14
d) 14 and 20
e) 14 and 22
Answer:
6 and 14 respectively
Explanation:
proton number = atomic number
mass number = proton number + neutron number
since
p.n = a.n = 6m.n = p.n + n.nm.n = 6 + 8 = 14m.n = 14An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the wa
Answer:
32.1
Explanation:
NOTE: You did not state the angle of incidence, and thus, I will be using 45° as my angle of incidence, all you need to do is replace it with your own value if it's different.
To solve this question, we are going to be using Snell's Law.
Snell's law describes the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
Snell's law is mathematically given as
sin(A1)/sin(A2) = n2/n1, where
n1 = incidence index
n2 = refracted index
A1 = incidence angle
A2 = refracted angle
The refraction index of oil is 1.15, and that of water is 1.33, so
if we take oil first,
sin A2 = (n1.sinA1)/n2
sin A2 = (1 * sin 45)/1.15
sin A2 = 0.7071/1.15
sin A2 = 0.6149
A2 = sin^-1 0.6149
A2 = 37.9°
Then
sin A3 = (1.15 * sin 37.9) / 1.33
sin A3 = (0.6149 * 1.15) / 1.33
sin A3 = 0.7071 / 1.33
sin A3 = 0.5317
A3 = sin^-1 0.5317
A3 = 32.1
If during the submerged weighing procedure air bubbles were to adhere to the object, how would the experimental results be affected
Answer:
see from this analysis, the apparent weight of the body is lower due to the push created by the air brujuleas
Explanation:
We will propose this exercise using Archimedes' principle, which establishes that the thrust on a body is equal to the volume of the desalted liquid.
B = ρ g V
The weight of a submerged body is the net force between the weight and the thrust
F_net = W - B
we can write the weight as a function of the density
ρ_body = m / V
m = ρ_body V
W = mg
W = ρ _body g V
we substitute
F_net= ( ρ_body - ρ _fluid) g V
In general this force is directed downwards, we can call this value the apparent weight of the body. This is the weight of the submerged body.
W_aparente = ( ρ_body - ρ _fluid) g V
If some air bubbles formed in this body, the net force of these bubbles is
F_net ’= #_bubbles ( ρ_fluido - ρ_air) g V’
this force is directed upwards
whereby the measured force is
F = W_aparente - F_air
As we can see from this analysis, the apparent weight of the body is lower due to the push created by the air brujuleas
An ideal spring hangs from the ceiling. A 1.95 kg mass is hung from the spring, stretching the spring a distance d=0.0865 m from its original length when it reaches equilibrium. The mass is then lifted up a distance L=0.0325 m from the equilibrium position and released. What is the kinetic energy of the mass at the instant it passes back through the equilibrium position?
Answer:
kinetic energy = 0.1168 J
Explanation:
From Hooke's law, we know that ;
F = kx
k = F/x
We are given ;
Mass; m = 1.95 kg
Spring stretch; d = x = 0.0865
So, Force = mg = 1.95 × 9.81
k = 1.95 × 9.81/0.0865 = 221.15 N/m
Now, initial energy is;
E1 = mgL + ½k(x - L)²
Also, final energy; E2 = ½kx² + ½mv²
From conservation of energy, E1 = E2
Thus;
mgL + ½k(x - L)² = ½kx² + ½mv²
Making the kinetic energy ½mv² the subject, we have;
½mv² = mgL + ½k(x - L)² - ½kx²
We are given L=0.0325 m
Plugging other relevant values, we have ;
½mv² = (1.95 × 9.81 × 0.0325) + (½ × 221.15(0.0865 - 0.0325)² - ½(221.15 × 0.0865²)
½mv² = 0.62170875 + 0.3224367 - 0.82734979375
½mv² = 0.1168 J
A particle has velocity v⃗1 v → 1 as it accelerates from 1 to 2. What is its velocity vector v⃗2 v → 2 as it moves away from point 2 on its way to point 3?
Answer:
The velocity of the particle will be downward.
Explanation:
Given that,
The velocity of a particle is v₁. It is accelerated from 1 to 2.
If it moves away from point 2 on its way then
We need to find the velocity of particle
According to figure,
A particle moves downward from 1 to 2 with the velocity v₁ and after that the particle moves downward from 2 to 3 with the velocity v₂.
Hence, The velocity of the particle will be downward.
The atomic mass number of copper is A=64. Assume that atoms in solid copper form a cubic crystal lattice. To envision this, imagine that you place atoms at the centers of tiny sugar cubes, then stack the little sugar cubes to form a big cube. If you dissolve the sugar, the atoms left behind are in a cubic crystal lattice. What is the smallest distance between two copper atoms?
Answer:
0.228 nm
Explanation:
Atomic mass number of copper = 64
but an atomic mass unit = 1.66 x 10^-27 kg
therefore, the mass of the copper atom m = 64 x 1.66 x 10^-27 kg = 1.06 x 10^-25 kg
The number of atoms in this mass n = ρ/m
where ρ is the density of copper = 8.96 x 10^3 kg/m^3
==> n = (8.96 x 10^3)/(1.06 x 10^-25) = 8.45 x 10^28 atoms/m^3
We know that the volume occupied by this amount of atoms n = [tex]a^{3}[/tex]
where a is the lattice constant
equating, we have
8.45 x 10^28 = [tex]a^{3}[/tex]
a = 4.389 x 10^9
we also know that
d = 1/a
where d is the smallest distance between the two copper atom.
d = 1/(4.389 x 10^9) = 2.28 x 10^-10 m
==> 0.228 nm
A race car is on a track has a velocity of 200 m/s. 15 seconds later the driver notices that he is going 350 m/s. What is his acceleration?
Answer:
initial velocity (u) = 200m/s
final velocity (v) = 350 m/s
time (t) = 15s
acceleration (a) = ?
NOW,
a=v-u/t
a= 350-200/15
a= 50/15
a= 3.3333
Explanation:
it's too easy just u need to understand the question . and go according to it's content .
main thing to memorize is it's simple formula.
I HAVE SOLVE THIS QNA. IN VERY
SIMPLE AND UNDERSTANDABLE FORM.
I høpë u hađ uņdērstøöď ťhìs şølutîóñ
:verý ×wəłł.
6° with the horizontal) at a steady speed of 4.0 m/s. Assuming a total mass of 75 kg (bicycle and Kasek), what must be Kasek's power output to climb the same hill at the same speed?
Answer:
Power, P = 307.31 W
Explanation:
It is given that,
Kasek climb at an angle of 6° with the horizontal at a steady speed of 4.0 m/s.
The total mass of bicycle and Kasek is 75 kg
We need to find the Kasek's power output to climb the same hill at the same speed. The angle is made with the horizontal. It means that,
F = F sinθ
So,
Power output is given by :
[tex]P=mg\sin\theta\times v\\\\P=75\times 9.8\times \sin(6)\times 4\\\\P=307.31\ W[/tex]
So, Kasek's power output to climb the same hill is 307.31 W.
g If the momentum of an electron doubles, by what factor would its de Broglie wavelength be multiplied
Explanation:
The de broglie wavelength is given by :
[tex]\lambda=\dfrac{h}{p}[/tex]
Here,
h is Planck's constant
p is momentum
Momentum and De-Broglie wavelength has inverse relationship. If momentum of an electron double, its wavelength gets half.
Two identical resistors were connected in parallel and their equivalent resistance was
4 ohm. If the two resistors were connected in series, then their equivalent resistance
(in ohm) would be:
Select one:
a. 30
b.4
c. 16
d. 8
O e. 2
Å
Answer:
C
Explanation:
Rt= total resistance
we know that 1/Rt=1/R1+1/R2(from ohm's law)
Since, Rt=4 and R1=R2
we will get,
1/4=2/R2
R2=8
when in series Rt=R1+R2,
So, Rt=8+8=16 ohm's
If the two resistors are connected in series, then their equivalent resistance (in ohm) will be 16 ohms
The correct answer to the question is Option C. 16 ohms
Fact from the questionSince the two resistors are identical, then
R₁ = R₂
Determination of the two resistors•Equivalent resistance (Rₜ) = 4 Ohms
•Resistor 1 (R₁) = Resistor 2 (R₂) =?
In parallel connection,
Rₜ = (R₁ × R₂) / (R₁ + R₂)
4 = (R₁ × R₁) / (R₁ + R₁)
4 = R₁² / 2R₁
4 = R₁ / 2
Cross multiply
R₁ = 4 × 2
R₁ = 8 Ohms
Thus,
R₂ = R₁ = 8 Ohms
Determination of the equivalent resistance in series•Resistor 1 (R₁) = 8 Ohms
•Resistor 2 (R₂) = 8 Ohms
•Equivalent resistance (Rₜ) =?
In series connection,
Rₜ = R₁ + R₂
Rₜ = 8 + 8
Rₜ = 16 Ohms
Thus, the correct answer to the question is Option C. 16 ohms
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An electron and a 0.033 0-kg bullet each have a velocity of magnitude 495 m/s, accurate to within 0.010 0%. Within what lower limit could we determine the position of each object along the direction of the velocity
Answer:
1.170*10^-3 m
3.23*10^-32 m
Explanation:
To solve this, we apply Heisenberg's uncertainty principle.
the principle states that, "if we know everything about where a particle is located, then we know nothing about its momentum, and vice versa." it also can be interpreted as "if the uncertainty of the position is small, then the uncertainty of the momentum is large, and vice versa"
Δp * Δx = h/4π
m(e).Δv * Δx = h/4π
If we make Δx the subject of formula, by rearranging, we have
Δx = h / 4π * m(e).Δv
on substituting the values, we have
for the electron
Δx = (6.63*10^-34) / 4 * 3.142 * 9.11*10^-31 * 4.95*10^-2
Δx = 6.63*10^-34 / 5.67*10^-31
Δx = 1.170*10^-3 m
for the bullet
Δx = (6.63*10^-34) / 4 * 3.142 * 0.033*10^-31 * 4.95*10^-2
Δx = 6.63*10^-34 / 0.021
Δx = 3.23*10^-32 m
therefore, we can say that the lower limits are 1.170*10^-3 m for the electron and 3.23*10^-32 for the bullet
3 holits = 5 gorfs
7 gorfs = 2 queets
How many queets are there in 43 holits?
Explanation:
43 holits × (5 gorfs / 3 holits) × (2 queets / 7 gorfs) ≈ 20.5 queets
Please help and thank you :)
Answer:
20 m/s.
Explanation:
Data obtained from the question include the following:
Initial position (d1) = 20 m
Final position (d2) = 60 m
Initial time (t1) = 1 sec
Final time (t2) = 3 secs
Velocity (v) =?
Next, we shall determine the change in position (Δd). This can be obtained as follow:
Initial position (d1) = 20 m
Final position (d2) = 60 m
Change in position (Δd) =?
Change in position (Δd) = d2 – d1
Change in position (Δd) = 60 – 20
Change in position (Δd) = 40 m
Next, we shall determine the change in time (Δt). This can be obtained as follow:
Initial time (t1) = 1 sec
Final time (t2) = 3 secs
Change in time (Δt) =?
Change in time (Δt) = t2 – t1
Change in time (Δt) = 3 – 1
Change in time (Δt) = 2 secs.
Finally, we shall determine the velocity of the object as follow:
Change in position (Δd) = 40 m
Change in time (Δt) = 2 secs.
Velocity (v) =?
Velocity (v) = Change in position (Δd) /Change in time (Δt)
v = Δd/Δt
v = 40/2
v = 20 m/s
Therefore, the velocity of the object between 1 and 3 secs is 20 m/s
Select the correct answer from each drop-down menu.
What forms of energy are involved when snow on a mountain breaks loose, resulting in an avalanche?
During an avalanche, the
energy of the snow on the mountain is converted into
energy as the snow cascades down.
Answer:
Gravitational potential energy is converted into kinetic energy
Explanation:
During an avalanche, the gravitational potential
energy of the snow on the mountain is converted into
kinetic energy as the snow cascades down.
The potential energy stored by the snow collected high in the mountain under the gravitational field created by our Earth, breaks loose and as it comes down acquiring velocity, it is converted into kinetic energy due to its accelerated motion
Which is one physical property that all stars have
Answer:
Star characteristics consider physical characteristics such as stellar mass, size, surface temperature, and luminosity .
Answer:
They are made of gases.
Explanation:
Edg 2020
a 5-ton bus stopped on a ramp at a 30-degree angle. What is the friction force with the ground, in newtons, to keep it from sliding down the slope?
Answer:
2500 N
Explanation:
Draw a free body diagram of the bus. There are three forces:
Weight force mg pulling down,
Normal force N pushing perpendicular to the ramp,
and friction force F pushing parallel to the ramp.
Sum of forces in the parallel direction:
∑F = ma
F − mg sin θ = 0
F = mg sin θ
F = (5000 N) (sin 30°)
F = 2500 N
Light from a helium-neon laser (λ = 633 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 2.5 m behind the slits. Eleven bright fringes are seen, spanning a distance of 54 mm. What is the spacing (in mm) between the slits?
Answer:
The value is [tex]d = 0.000293 \ m[/tex]
Explanation:
From the question we are told that
The wavelength is [tex]\lambda = 633 \ nm = 633 *10^{-9} \ m[/tex]
The distance of the screen is [tex]D = 2.5 \ m[/tex]
The order of the bright fringes is [tex]n = 10[/tex] (10 fringe + central maximum = eleven bright fringes )
The distance between the fringe is [tex]y = 54 \ mm = 0.054 \ m[/tex]
Generally the condition for constructive interference is
[tex]d sin \theta = n * \lambda[/tex]
=> [tex]d = \frac{n * \lambda}{sin \theta}[/tex]
Now from the SOHCAHTOA rule the angle [tex]sin \theta[/tex] is mathematically represented as
[tex]sin (\theta) = \frac{y}{D}[/tex]
So
[tex]d = \frac{n * \lambda}{\frac{y}{D} }[/tex]
=> [tex]d = \frac{10 * 633 *10^{-9}}{\frac{0.054}{ 2.5} }[/tex]
=> [tex]d = 0.000293 \ m[/tex]
If a mass on a spring is 16 kg and the spring constant is 4 N/m, what would be its period?
Explanation:
T = 2π√(m/k)
T = 2π√(16 kg / 4 N/m)
T = 4π s
T ≈ 12.6 s
A 68.5 kg astronaut is doing a repair in space on the orbiting space station. He throws a 2.25 kg tool with a speed of 3.20 m / s relative to the space station. With what speed and direction will the astronaut begin to move?
Explanation:
Momentum is conserved.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Initially, both the astronaut and the tool are at rest, so u₁ = u₂ = 0 m/s.
After throwing the tool, the tool has a velocity of v₂ = 3.20 m/s.
(68.5 kg) (0 m/s) + (2.25 kg) (0 m/s) = (68.5 kg) v + (2.25 kg) (3.20 m/s)
0 = (68.5 kg) v + 7.2 kg m/s
v = -0.105 m/s
The astronaut moves at a speed of 0.105 m/s in the opposite direction.
The speed and the direction of the astronaut is 0.105 m/s in opposite direction to the motion of the tool.
Note: The momentum of the astronaut is equal and opposite to the momentum of the tool
To calculate the speed and the direction of the astronaut, we use the formula below.
Formula:
MV = -mv.............. Equation 1Where:
M = mass of the astronautV = speed of the astronautm = mass of the toolv = speed of the tool.make V the subject of the equation
V = mv/M................. Equation 2From the question,
Given:
m = 2.25 kgM = 68.5 kgv = 3.2 m/sSubstitute these values into equation 2
V = (2.25×3.2)/68.5V = 0.105 m/s in opposite direction to the speed of the tool.Hence, The speed and the direction of the astronaut is 0.105 m/s in opposite direction to the motion of the tool.
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A teacher performing a demonstration finds that a piece of cork displaces 44.5ml of water. The piece of cork has a mass of 11.1g. What is density of the cork
Explanation:
Density = mass / volume
ρ = 11.1 g / 44.5 mL
ρ = 0.249 g/mL
What properties do you think a spoon must have for it to be
useful as an eating tool? What additional properties must an edible spoon
have?
Answer:
eating instrument must be: HARDNESS, INERT, NOT TOXIC
eating tools: digested by the body
Explanation:
An eating instrument must be able to contain food, so it must have a good HARDNESS, besides it must be poorly absorbent of heat and the most important must be INERT, not react with food or be NOT TOXIC to humans.
Additionally, for a spoon to be edible, it must be able to be digested by the body, in general they are made with a starch base, so that the non-digestible parts of it have not been toxic to the body and can be eliminated from it.
There are numerous features of a spoon but these properties must an edible spoon
have
A spoon must be Sizable in nature to be use on the mouthA spoon must not contain an fatal substance as it will be used for eating A spoon Strong and not weather under pressure of heat A spoon should be Durable to stand the test of timeFor more information on this visit
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A 1.07 H inductor is connected in series with a fluorescent lamp to limit the current drawn by the lamp. If the combination is connected to a 28.9 Hz, 170 V line, and if the voltage across the lamp is to be 17.6 V, what is the current in the circuit
Answer:
0.784 A
Explanation:
From the question,
Note that the current in the circuit is the same as the current flowing through the inductor since they are both connected in series.
I = VL/XL....................... Equation 1
Where I = current flowing through the circuit, VL = Voltage drop across the inductor, XL = reactance of the inductor.
XL = 2πfL................. Equation 2
Given: f = 28.9 Hz, L = 1.07 H, π = 3.143
XL = 2(3.143)(28.9)(1.07)
XL = 194.38 Ω.
VL = V-Vf
VL = 170-17.6
VL = 152.4 V
Substitute these values into equation 1
I = 152.4/194.38
I = 0.784 A
The current in the circuit when combination is connected should be 0.784 A.
Calculation of the current:SInce
we know that
I = VL/XL....................... Equation 1
Here,
I = current flowing through the circuit,
VL = Voltage drop across the inductor,
XL = reactance of the inductor.
And,
XL = 2πfL................. Equation 2
Here
f = 28.9 Hz, L = 1.07 H, π = 3.143
So,
XL = 2(3.143)(28.9)(1.07)
XL = 194.38 Ω.
Now
VL = V-Vf
VL = 170-17.6
VL = 152.4 V
Now
I = 152.4/194.38
I = 0.784 A
hence, The current in the circuit when combination is connected should be 0.784 A.
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Two long parallel wires are separated by 6.0 mm. The current in one of the wires is twice the other current. If the magnitude of the force on a 3.0-m length of one of the wires is equal to 8.0 μN, what is the greater of the two currents?
Answer:
Explanation:
Magnitude of force per unit length of wire on each of wires
= μ₀ x 2 i₁ x i₂ / 4π r where i₁ and i₂ are current in the two wires , r is distance between the two and μ₀ is permeability .
Putting the values ,
force per unit length = 10⁻⁷ x 2 x i x 2i / ( 6 x 10⁻³ )
= .67 i² x 10⁻⁴
force on 3 m length
= 3 x .67 x 10⁻⁴ i²
Given ,
8 x 10⁻⁶ = 3 x .67 x 10⁻⁴ i²
i² = 3.98 x 10⁻²
i = 1.995 x 10⁻¹
= .1995
= 0.2 A approx .
2 i = .4 A Ans .
The greater current is 0.4 A
Since the two long wires are parallel, the magnetic force, F on each wire is given by
F = μ₀I₁I₂L/2πd where μ₀ = permeability of free space = 4π × 10⁻⁷ H/m, I₁ = current in first wire, I₂ = current in second wire, L = length of section of wires = 3.0 m and d = separation distance of the wires = 6.0 mm = 6.0 × 10⁻³ m.
Given that F = 8.0 μN = 8.0 × 10⁻⁶ N and I₂ = 2I₁ (the current in one wire is twice the current in the other wire), we have
F = μ₀I₁I₂L/2πd
F = μ₀ 2I₁I₁L/2πd
F = μ₀I₁²L/πd
Since we require the current in the wire, we make I₁ subject of the formula.
So, I₁ = √(Fπd/μ₀L)
Substituting the values of the variables into the equation, we have
I₁ = √(Fπd/μ₀L)
I₁ = √[8.0 × 10⁻⁶ N × π × 6.0 × 10⁻³ m/(4π × 10⁻⁷ H/m × 3.0 m)]
I₁ = √[48.0π × 10⁻⁹ Nm/12π × 10⁻⁷ H]
I₁ = √[4 × 10⁻² Nm/H]
I₁ = 2 × 10⁻¹ A
I₁ = 0.2 A
Since I₂ is the greater current and I₂ = 2I₁,
I₂ = 2 × 0.2 A
I₂ = 0.4 A
So, the greater current is 0.4 A
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What does a constant velocity look like on a displacement vs time graph?
Answer:
A line with slope equal to the velocity.
Explanation:
If one is in the presence of constant velocity, that means that at the quotient between displacement and time elapsed is a constant value, therefore one can write the following equation:
[tex]\frac{displacement}{time} =constant[/tex]
therefore, solving for displacement we get:
[tex]displacement= constant \,*\, time[/tex]
which if plotted with displacement (D) on the vertical axis and time (t) on the horizontal axis, renders a line with slope equal to the constant value of the velocity (v):
[tex]D=v\,*\,t[/tex]
A stretched string is observed to vibrate in three equal segments when driven by a 480-Hz oscillator. What is the fundamental frequency of vibration for this string
Answer:
160 Hz
Explanation:
Fundamental frequency, [tex]f_{0}[/tex], is the lowest frequency that can be obtained from the stretched string. While higher frequencies are termed harmonics or overtones.
Since the string has three equal segments, the frequency generated, [tex]f_{2}[/tex], is the second harmonic but third overtone.
From the relationship between [tex]f_{0}[/tex] and [tex]f_{2}[/tex], we have;
[tex]f_{2}[/tex] = 3[tex]f_{0}[/tex]
⇒ 480 = 3[tex]f_{0}[/tex]
[tex]f_{0}[/tex] = 160
The fundamental frequency of vibration for the string is 160 Hz.
In an experiment you measure a first-order red line for Hydrogen at an angle difference of ΔΘ = 22.78o. The diffraction grating you are using has 5900 lines per cm.
a) What is the wavelength of this light?
b) What is the value of Rydberg's constant for this measurement?
Answer:
a) wavelength = 656.3 nm
b) the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹
Explanation:
Given that;
angle of diffraction Θₓ = 22.78°
incident angle Θ₁ = 0
slit separation d = 5900 lines per cm = 1/5900 cm = 10⁻²/5900 m = 0.01/5900 m
order of diffraction n = 1
wavelength λ = ?
to find the wavelength, we use the expression
λ = d (sinΘ₁ + sinΘₓ) / n
To find the wavelength λ;
λ = 0.01/5900 × (sin0 + sin22.78° )
λ = 6.5626 × 10⁻⁷ m
λ = 656.3 x 10⁻⁹ m
∴ λ = 656.3 nm
b)
According Balnur's series spectral lines; n₁ = 3, n₂ = 2 and
λ = R [ 1/n₂² - 1/n₁²]
where R is Rydberg's constant
from λ = R [ 1/n₂² - 1/n₁²]
R = 1/λ [n₂²n₁² / n₁² - n₂²]
R = 10⁹/ 656.3 [ 9 × 4 / 9 - 4 ]
R = 1.097 × 10⁷ m⁻¹
Therefore the value of Rydberg's constant for this measurement is 1.097 × 10⁷ m⁻¹
An electron and a proton have their masses in the ratio 1:1840. What will be the ratio of their kinetic energy if they have equal momentum?
Answer:
1840:1
Explanation:
If m is the mass of the electron, and 1840m is the mass of the proton, then:
p₁ = p₂
m₁v₁ = m₂v₂
m v₁ = 1840m v₂
v₁ = 1840 v₂
The kinetic energy of the electron is:
KE₁ = ½ m₁ v₁²
KE₁ = ½ m (1840 v)²
KE₁ = 1692800 mv²
The kinetic energy of the proton is:
KE₂ = ½ m₂ v₂²
KE₂ = ½ (1840m) v₂²
KE₂ = 920 mv²
The ratio of the kinetic energies is:
KE₁ / KE₂
(1692800 mv²) / (920 mv²)
1840:1
(b) A ball is thrown upward from the top of a 30 m tower with initial velocity 90 m/s at an angle
O = 20°
Find the time to reach the ground
(Smarks)
Find the magnitude and direction of the velocity at the moment of impact (5 marks)?
Answer:
7.14 s
93.2 m/s, 24.9° below the horizontal
Explanation:
Given in the y direction:
Δy = -30 m
v₀ = 90 m/s sin 20° ≈ 30.8 m/s
a = -9.8 m/s²
Find: t
Δy = v₀ t + ½ at²
-30 m = (30.8 m/s) t + ½ (-9.8 m/s²) t²
4.9t² − 30.8t − 30 = 0
t = [ 30.8 ± √((-30.8)² − 4(4.9)(-30)) ] / 2(4.9)
t = 7.14 s
Find: vᵧ
v² = v₀² + 2aΔy
vᵧ² = (30.8 m/s)² + 2 (-9.8 m/s²) (-30 m)
vᵧ = -39.2 m/s
The magnitude of the velocity is:
v² = vₓ² + vᵧ²
v² = (90 m/s cos 20°)² + (-39.2 m/s)²
v = 93.2 m/s
The direction of the velocity is:
tan θ = vᵧ / vₓ
tan θ = (-39.2 m/s) / (90 m/s cos 20°)
θ = -24.9°
Roy took 5 hours to complete a journey. For the first 2 hours,
he travelled at an average speed of 65 km/h. For the rest of
the journey, he travelled at an average speed of 78 km/h. What
was the total distance of the journey?
Answer:
use the distance formula d=v*t
d= distance
v = velocity
t = time = t1 + t2 = 2h +3h = 5 hours (total time given)
At 65 km/h distance (d1) answer:
d1 = (65 km/h)*( 2h) = 130 km
Total Distance:
so d1 + d2 = Dtotal
Dtotal = 130 km + (78 km/h)*3 = 130 km + 234 km = 364 km