The stopping potential for electrons emitted from a photosensitive surface illuminated by light of a wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is: 

CONCEPT:

According to the equation of photoelectric effect equation we have;

 = ϕ  + eV_s      -----(1)

Here we have h is Planck's constant, c is the velocity of light, λ  is the wavelength, ϕ  is the work function and V_s is the stopping potential.

CALCULATION:

Given: Wavelength, λ₁ = 491 nm

Stopping potential, V_s1 = 0.710 V

Stopping potential, V_s2 = 1.43 V

and hc = 1240 eV nm

Now, from equation (1) we have;

⇒ eV_s1 =      -----(2)

and change the wavelength we have;

 eVs2 =        -----(3)

Now, by subtracting equation (2) by (3) we have;

 = 

⇒ 

⇒ 

Now, on putting the given values we have;

​​

⇒ (0.710 - 1.43 ) = 1240 

⇒ -0.72 = 1240 ​​

⇒ 

⇒  = 0.00203 + 0.00058

⇒  = 0.00261

⇒ λ2 = 383.1417

⇒ λ2  382 nm

Hence, option 3) is the correct answer.