A photoelectric experiment is performed by separately shining a laser of 450 nm
(blue light) and 560 nm (yellow light) on a metal surface and measuring the
number and kinetic energy of the ejected electrons.
The threshold frequency of
the metal is 6.00•10^14 Hz.
a. Compare the number of electrons ejected from the metal for each of the
lasers when directed at the metal for the same amount of time. Explain
How do you find the number of electrons from all of this? I only know how to solve for wavelength and energy??
I don't think you are to find the number of electrons ejected; I think you are to compare. That is, I think that one beam ejects more or less electrons than the other and you tell that from the threshold frequency.
http://en.wikipedia.org/wiki/Photoelectric_effect
To find the number of electrons ejected from the metal for each laser, we need to understand the concept of the photoelectric effect. The photoelectric effect states that when light of sufficient energy (or frequency) is incident on a metal surface, it can eject electrons from the metal.
In this case, we are given the wavelength (450 nm and 560 nm) and the threshold frequency (6.00•10^14 Hz) of the metal.
To compare the number of electrons ejected for each laser, we rely on two important principles:
1. The energy of a photon can be calculated using the equation: E = hc/λ, where:
- E is the energy of the photon,
- h is Planck's constant (approximately 6.626 x 10^-34 J·s),
- c is the speed of light (approximately 3.0 x 10^8 m/s),
- λ is the wavelength of the light in meters.
2. The minimum energy required to eject an electron, known as the threshold energy (E_threshold), is related to the threshold frequency (f_threshold) by the equation: E_threshold = hf_threshold, where:
- E_threshold is the threshold energy,
- h is Planck's constant,
- f_threshold is the threshold frequency.
To determine the number of electrons ejected, we can compare the energies of the photons from each laser to the threshold energy of the metal.
Let's calculate the energy of the photons for each laser:
For the blue light (450 nm):
1. Convert wavelength to meters: λ = 450 nm = 450 x 10^-9 m.
2. Calculate the energy using the equation: E = hc/λ.
- E_blue = (6.626 x 10^-34 J·s) * (3.0 x 10^8 m/s) / (450 x 10^-9 m).
For the yellow light (560 nm):
1. Convert wavelength to meters: λ = 560 nm = 560 x 10^-9 m.
2. Calculate the energy using the equation: E = hc/λ.
- E_yellow = (6.626 x 10^-34 J·s) * (3.0 x 10^8 m/s) / (560 x 10^-9 m).
Compare the energy of each photon to the threshold energy of the metal.
If the energy of a photon is greater than or equal to the threshold energy, electrons will be ejected. If the energy is less than the threshold energy, no electrons will be ejected.
From this information, we can determine the number of electrons ejected for each laser when directed at the metal for the same amount of time.