A metal surface is struck with light of wavelength 430 nm releasing a stream of electrons. If the 430 nm light is replaced by 380 nm light of the same intensity, what is the result?
a.
no change to the emitted electrons
b.
emitted electrons are more energetic
c.
more electrons are emitted in a given time interval
d.
fewer electrons are emitted in a given time interval
e.
emitted electrons are less energetic
b.
emitted electrons are more energetic
Einstein's relation for phptoelectric effect: hc/λ=v W= KE,
λ↓ KE↑
To answer this question, we need to understand the principles of the photoelectric effect. The photoelectric effect is a phenomenon where electrons are liberated from the surface of a material when it is exposed to light.
According to the photoelectric effect, the energy of the liberated electrons depends on the frequency (or equivalently, wavelength) of the incident light. Higher frequency light (shorter wavelength) has more energy per photon than lower frequency light (longer wavelength).
In this case, we are comparing light of two different wavelengths, 430 nm and 380 nm.
To determine the effect of changing the wavelength, we need to compare the energies of the photons associated with each wavelength. The energy of a photon can be calculated using the formula E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength.
Let's calculate the energies of the photons for both wavelengths:
For 430 nm light:
E1 = hc/λ1 = (6.626 x 10^-34 J·s * 3.0 x 10^8 m/s) / (430 x 10^-9 m)
For 380 nm light:
E2 = hc/λ2 = (6.626 x 10^-34 J·s * 3.0 x 10^8 m/s) / (380 x 10^-9 m)
By calculating these values, we find that E1 > E2, indicating that the photons associated with 430 nm light have a higher energy compared to 380 nm light.
Now, we can determine the effect of changing the wavelength on the emitted electrons:
When the metal surface is struck by light, electrons are emitted if the incident energy is sufficient to overcome the work function of the material (which is the minimum energy required to liberate an electron). If the incident light energy exceeds the work function, the excess energy becomes the kinetic energy of the emitted electrons.
Since the energy of the photons associated with 430 nm light is larger than the energy of the photons associated with 380 nm light, the 430 nm light is more likely to have sufficient energy to overcome the work function of the metal surface. Therefore, choice (e) - emitted electrons are less energetic - is the correct answer.
In summary, when the 430 nm light is replaced by 380 nm light of the same intensity, the result is that the emitted electrons will be less energetic.