Question

The kinetic energy of photoelectrons increases by 0.52 eV when the wavelength of incident light is changed from 500 nm to another web length which is approximately

• A. 1250 mm
• B. 700 nm
• C. 1000 nm
• D. 400 nm

Answer 1

Answer: (D)

400 nm

Answer 2

E = hc/λ
where E is the energy of the photon, h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3 x 108 m/s), and λ is the wavelength of the light.
Let's convert the energy difference from electron volts (eV) to joules (J):
0.52 eV = 0.52 x 1.6 x 10-19 J (since 1 eV = 1.6 x 10-19 J)
0.52 eV = 8.32 x 10-20 J
Now, let's calculate the initial energy and the new energy using the equation E = hc/λ.
For the initial wavelength of 500 nm (500 x 10-9 m):
Einitial = (6.626 x 10-34 J·s) x (3 x 108 m/s) / (500 x 10-9 m)
Einitial ≈ 3.9768 x 10-19 J
For the new wavelength (let's call it λ_new):
Enew = (6.626 x 10-34 J·s) x (3 x 108 m/s) / λ_new
Now, we can set up the equation using the energy difference:
Enew - Einitial = 8.32 x 10-20 J
(6.626 x 10-34 J·s) x (3 x 108 m/s) / λ_new - 3.9768 x 10-19 J = 8.32 x 10-20 J
Simplifying the equation: (6.626 x 10-34 J·s) x (3 x 108 m/s) = 8.32 x 10-20 J + 3.9768 x 10-19 J
(6.626 x 10-34 J·s) x (3 x 108 m/s) = 4.8 x 10-19 J
Now, solving for λnew:
λnew = (6.626 x 10-34 J·s) x (3 x 10^8 m/s) / (4.8 x 10-19 J)
λnew ≈ 4.140625 x 10-7 m
To determine which option is approximately equal to the new wavelength, let's convert it to the corresponding unit:
λnew ≈ 414 nm
Comparing this result with the given answer choices, we can conclude that the approximate new wavelength is 400 nm.
Therefore, the correct option is (D) 400 nm.