Planck's problem (waves and frequency)

  • Thread starter lemin_rew
  • Start date
  • Tags
    Frequency
In summary: B (i used 4 hz for B) = i got 7.2x10^-17 m/s"The equation says that the difference in speed is 2.06x10^-17m/s.
  • #1
lemin_rew
27
0

Homework Statement



the frequency of A is doubled the threshold frequency of B.
if the wavelength of B is half that of A, what is the difference in speed?



Homework Equations



E=hv
E=1/2mu^2
c=vλ

The Attempt at a Solution


the answer is : square root of 3
i tried different ways,,,but just not getting anywhere.
please help
 
Physics news on Phys.org
  • #2
It helps if you specify your problem completely.
I take it you mean this is a photoelectric effect problem?

light A has double the threshold frequency of light B (what determines the threshold frequency? Write it down.)

wavelength of B is half that of A (you can write that down?)

what is the difference in speed ... of what?
the two kinds of light? That would be zero.
the speed of electrons ejected by each type?
... do you have the relation between the energy of the incoming photon and the kinetic energy of the ejected electron?

"I tried different ways" does not tell us what you tried... we cannot help you if you don't tell us.
 
  • #3
Simon Bridge said:
It helps if you specify your problem completely.
I take it you mean this is a photoelectric effect problem?

light A has double the threshold frequency of light B (what determines the threshold frequency? Write it down.)

wavelength of B is half that of A (you can write that down?)

what is the difference in speed ... of what?
the two kinds of light? That would be zero.
the speed of electrons ejected by each type?
... do you have the relation between the energy of the incoming photon and the kinetic energy of the ejected electron?

"I tried different ways" does not tell us what you tried... we cannot help you if you don't tell us.

OH YUP. sorry about that. this is the exact question.

Two photons (A&B) strike a metal surface and eject an electron.

The frequency of photon A is double the threshold frequency, while the wavelength of
photon B is ½ that of photon A.

What is the difference in speed (by what factor) of the electrons?

Express answer as a whole number.

my attempts:
i said the thresold frequency is = 1 hz
then A's frequency must be =2 hz
then the λ of A = (3.0x10^8m/s)/(2hz)=1.5x10^8m
B's λ is 1/2 of A = (1.5x10^8m/s)/2 = 0.75 x 10^8m
B's f is = (3.0x10^8m/s)/(0.75 x 10^8m) =4hz
i used the equation ΔEA=1/2mu^2 ΔEB=1/2mu^2 (i cancled m from noth equations)
ΔEA=1/2u^2=hv
[itex]\sqrt{}hv/0.5[/itex]=u
for A = [itex]\sqrt{}(6.62x10^-34)(2)/(0.5)[/itex] = 5.14x10^-17m/s
i repeated the same thing for B (i used 4 hz for B) = i got 7.2x10^-17 m/s
its asking for the difference in speed
(7.2x10^-17)-(5.14x10^-17)=2.06x10^-17m/s
I'm no near the answer [itex]\sqrt{}3[/itex]
 
  • #4
lemin_rew said:
my attempts:
i said the thresold frequency is = 1 hz
why choose 1Hz? Why not just leave it as ##\nu_{thresh}## or ##\nu_0## or something?
then A's frequency must be =2 hz
then the λ of A = (3.0x10^8m/s)/(2hz)=1.5x10^8m
B's λ is 1/2 of A = (1.5x10^8m/s)/2 = 0.75 x 10^8m
B's f is = (3.0x10^8m/s)/(0.75 x 10^8m) =4hz
i used the equation ΔEA=1/2mu^2 ΔEB=1/2mu^2 (i cancled m from noth equations)
ΔEA=1/2u^2=hv
Doesn't this mean that all the energy of the incoming photon goes to the kinetic energy in the ejected electron?
Doesn't the work function have a say in this?
 
  • #5


Planck's problem involves understanding the relationship between waves and frequency. According to Planck's equation, E=hv, where E is energy, h is Planck's constant, and v is frequency. This equation shows that as frequency increases, energy also increases. Additionally, the equation E=1/2mu^2, where m is mass and u is velocity, shows that energy is also related to the speed of the wave.

In the given scenario, the frequency of A is doubled, meaning that its energy has also doubled. This also means that the threshold frequency of B, where it can emit electrons, has also doubled. Furthermore, the wavelength of B is half that of A, which means that the speed of B is twice that of A.

To find the difference in speed, we can use the equation c=vλ, where c is the speed of light. Plugging in the values, we get c=2v(λ/2)=vλ. This shows that the speed of B is equal to the speed of light, while the speed of A is half the speed of light. Therefore, the difference in speed is the square root of 3 times the speed of light.

In conclusion, Planck's problem helps us understand the relationship between waves, frequency, and energy. The given scenario can be solved by using equations that relate these variables, and the difference in speed can be found by understanding the concept of speed of light and the given wavelengths.
 

1. What is Planck's problem in relation to waves and frequency?

Planck's problem refers to the question of how the energy of a wave is related to its frequency. This was a major challenge in understanding the behavior of electromagnetic waves, until Max Planck proposed his theory of quantization in 1900.

2. How did Max Planck solve the problem of waves and frequency?

Max Planck proposed that energy is not continuous, but is instead made up of tiny discrete units called quanta. He also introduced the concept of Planck's constant, which relates the energy of a photon to its frequency. This theory laid the foundation for quantum mechanics and helped to explain the behavior of waves and particles at the atomic level.

3. What impact did Planck's solution have on the field of physics?

Planck's solution to the problem of waves and frequency revolutionized the field of physics. It provided a new understanding of the behavior of electromagnetic radiation and led to the development of quantum mechanics, which has had a profound impact on modern technology and our understanding of the universe.

4. Can Planck's problem be applied to other types of waves besides electromagnetic waves?

Yes, Planck's theory of quantization can be applied to other types of waves, such as sound waves. In fact, it has been shown that the energy of a sound wave is also quantized, with the frequency of the wave determining the energy of each quantum.

5. Is Planck's problem still relevant in modern physics?

Yes, Planck's problem is still a relevant topic in modern physics. While his theory of quantization has been expanded upon and refined over the years, it remains an essential part of our understanding of the behavior of waves and particles at the atomic level. It also continues to play a crucial role in the development of new technologies, such as quantum computing.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
955
  • Introductory Physics Homework Help
Replies
1
Views
957
  • Introductory Physics Homework Help
Replies
5
Views
899
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
860
Back
Top