A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are and , respectively. If the ratio and the work function of the metal is nearly

Question

A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are $u_{1}$ and $u_{2}$ , respectively. If the ratio $u_{1} : u_{2} = 2 : 1,$ and $h c = 1240 eV nm,$ the work function of the metal is nearly [2014]

Smart Achievers · Accepted Answer

(1)

Here, $\frac{h C}{λ_{1}} - ϕ = \frac{1}{2} m u_{1}^{2}$ $\dots (i)$

and $\frac{h C}{λ_{2}} - ϕ = \frac{1}{2} m u_{2}^{2}$ $\dots (i i)$

Dividing equation (i) by (ii),

$\frac{\frac{h C}{λ_{1}} - ϕ}{\frac{h C}{λ_{2}} - ϕ} = \frac{u_{1}^{2}}{u_{2}^{2}}$

$∴$ $\frac{\frac{1240}{248} - ϕ}{\frac{1240}{310} - ϕ} = \frac{4}{1}$

$∴$ $\frac{1240}{248} - ϕ = 4 \times \frac{1240}{310} - 4 ϕ$

$∴$ $ϕ = 3.7 eV$

Hence, the work function of the metal is nearly, $ϕ = 3.7 eV$

Solution

1 3.7 eV

2 3.2 eV

3 2.8 eV

4 2.5 eV

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