JEE Advanced 2016Paper 2
- Exam
- JEE Advanced
- Year
- 2016
- Paper
- Paper 2
- Subject
- Physics
- Chapter
- Dual Nature of Matter
JEE Advanced 2016 · Paper 2 · Physics · Dual Nature of Matter
Light of wavelength λ _ ph falls on a cathode plate inside a vacuum...
Light of wavelength falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is and the anode is a wire mesh of conducting material kept at a distance d from the cathode. A potential difference V is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is which of the following statement(s) is(are) true ?
Options
- AFor large potential difference \left(\text{V} ≫ \dfrac{ϕ}{\text{e}}\right) , {λ}_{\text{e}} is approximately halved if V is made four times
- B{λ}_{\text{e}} increases at the same rate as {λ}_{\text{ph}} for {λ}_{\text{ph}} < \dfrac{\text{hc}}{ϕ}
- C{λ}_{ⅇ} is approximately halved, if d is doubled
- D{λ}_{ⅇ} decreases with increase in ϕ and {λ}_{\text{ph}}
Correct answer
A. For large potential difference \left(\text{V} ≫ \dfrac{ϕ}{\text{e}}\right) , {λ}_{\text{e}} is approximately halved if V is made four times
Step-by-step solution
{K}_\max = \dfrac{hc}{{λ}_{Ph}} - ϕ
Kinetic energy of reaching the anode will be
K = \dfrac{hc}{{λ}_{Ph}} - ϕ + eV
Now {λ}_{e} = \dfrac{h}{\sqrt{2mK}} = \dfrac{h}{\sqrt{2m\left(\dfrac{hc}{{λ}_{Ph}} - ϕ + eV\right)}}
If
{λ}_{e} = \dfrac{h}{\sqrt{2m\left(\dfrac{hc}{{λ}_{Ph}} + eV\right)}}
If
{\left({λ}_{e}\right)}_{f} ≃ \dfrac{{\left({λ}_{e}\right)}_{i}}{2}
Kinetic energy of reaching the anode will be
K = \dfrac{hc}{{λ}_{Ph}} - ϕ + eV
Now {λ}_{e} = \dfrac{h}{\sqrt{2mK}} = \dfrac{h}{\sqrt{2m\left(\dfrac{hc}{{λ}_{Ph}} - ϕ + eV\right)}}
If
{λ}_{e} = \dfrac{h}{\sqrt{2m\left(\dfrac{hc}{{λ}_{Ph}} + eV\right)}}
If
{\left({λ}_{e}\right)}_{f} ≃ \dfrac{{\left({λ}_{e}\right)}_{i}}{2}