Question

Ultraviolet light of wavelength $2271\stackrel{o}{\text{A}}$ from a $100W$ mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is $-1.3V$, estimate the work function of the metal. How would the photo-cell respond to a high-intensity$\left(\sim {10}^5\text{W}{\text{m}}^{\text{- 2}}\right)$ red light of wavelength $6328\stackrel{0}{\text{A}}$ produced by a He-Ne laser? $\left(h=6.63\times {10}^{-34}\text{js,}c=3\times {10}^8\text{m/s}\right)$

Answer 1

Given:

The wavelength of the light is $2271\stackrel{o}{A}$

The power of the laser is $100W$.

Stopping potential is $-1.3V$.

The energy required for the emission is:

$W=\frac{hc}{\lambda }-e{V}_o$

$W=\frac{6.6\times {10}^{-34}\times 3\times {10}^8}{2271\times {10}^{-10}}-1.6\times {10}^{-19}\times 1.3$

$W=6.64\times {10}^{-19}J$

$W=4.15eV$

The threshold frequency can be obtained as:

${\nu }_o=\frac{W}{h}$

${\nu }_o=\frac{6.64\times {10}^{-19}}{6.6\times 10-34}$

$=1.006\times {10}^{15}Hz$

The frequency of the red light is about $4.74\times {10}^{14}Hz$

Since the frequency of the incident light required is more than that of the red light, the photocell would respond to the incident light.