Question

When a metallic surface is illuminated with monochromatic light of wavelength λ, stopping potential for photoelectric current is 3 V₀. When the same metallic surface is illuminated with a light of wavelength 2λ, the stopping potential is V₀. The threshold wavelength for the surface is-

• A. 6λ
• B. 4λ
• C. 4λ/3
• D. 8λ

Answer 1

Answer: (B)

4λ

Answer 2

3V₀ = $\frac { \mathrm { hc } } { \mathrm { e } \lambda }$ – $\frac { \mathrm { hc } } { \mathrm { e } \lambda _ { 0 } }$ ...(1)

V₀ = $\frac { \mathrm { hc } } { 2 \mathrm { e } \lambda }$ –$\frac { \mathrm { hc } } { \mathrm { e } \lambda _ { 0 } }$ ...(2)

⇒ =

$\frac { 3 } { 2 }$ –=– $\frac { \mathrm { hc } } { \mathrm { e } \lambda _ { 0 } }$

$\frac { 3 } { 2 \lambda }$– $\frac { 3 } { \lambda _ { 0 } }$ = $\frac { 1 } { \lambda }$ – $\frac { 1 } { \lambda _ { 0 } }$

$\frac { 2 } { \lambda _ { 0 } }$= $\frac { 1 } { 2 \lambda }$

λ₀ = 4λ