Question

All electrons ejected from a metallic surface by the incident light of wavelength $200\text{nm}$ can be stopped before just travelling $1\text{m}$ in the direction of uniform electric field of $4{\text{NC}}^{-1}$. The work function of the surface is:

• A. $4.2\text{eV}$
• B. $6.2\text{eV}$
• C. $3.2\text{eV}$
• D. $2.2\text{eV}$

Answer 1

The correct option is D $2.2\text{eV}$

Retarding force on the electrons having maximum energy,

$F=qE$

So, retardation,

$a=\frac{F}{m}=\frac{qE}{m}...\left(1\right)$

Further,

$v^2-u^2=2as$

$\Rightarrow 0^2-u^2=2\times (-\frac{qE}{m})\times 1\left[\text{From}\right(1\left)\right]$

$\Rightarrow K{E}_{\text{max}}=\frac{1}{2}m{u}^2=qE...\left(2\right)$

Also,

${\varphi }_o=\frac{hc}{\lambda }-K{E}_{\text{max}}$

$\Rightarrow {\varphi }_o=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{200\times {10}^{-9}}-1.6\times {10}^{-19}\times 4\left[\text{From}\right(2\left)\right]$

$\Rightarrow {\varphi }_o=3.5\times {10}^{-19}\text{J}=2.2\text{eV}$
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