Question

Light with a wavelength of 395 nm illuminates a metal cathode. The maximum kinetic energy of the emitted electrons is 0.76 eV . Part A What is the longest wavelength of light that will cause electrons to be emitted from this cathode

Answer 1

Answer:

520.8 nm

Explanation:

We are given that

$\lambda=395 nm=395\times 10^{-9} m$

1 nm=$10^{-9} m$

Maximum kinetic energy,$K_{max}=0.76 eV=0.76\times 1.6\times 10^{-19}$ V

$1 e=1.6\times 10^{-19} C$

We have to find the maximum wavelength of light.

We know that

$h\nu=\frac{hc}{\lambda_0}+K_{max}$

Where $c=3\times 10^8 m/s$

$h=6.625\times 10^{-34}$

$6.625\times 10^{-34}\times \frac{3\times 10^8}{395\times 10^{-9}}=\frac{6.625\times 10^{-34}\times 3\times 10^8}{\lambda_0}+0.76\times 1.6\times10^{-19}$

$6.625\times 10^{-34}\times \frac{3\times 10^8}{395\times 10^{-9}}- 0.76\times 1.6\times10^{-19}=\frac{6.625\times 10^{-34}\times 3\times 10^8}{\lambda_0}$

$\lambda_0=\frac{6.625\times 10^{-34}\times 3\times 10^8}{6.625\times 10^{-34}\times \frac{3\times 10^8}{395\times 10^{-9}}- 0.76\times 1.6\times10^{-19}}$

$\lambda_0=5.208\times 10^{-7} m$=520.8 nm

Answer 2

The longest wavelength of light that will cause electrons to be emitted from this cathode should be considered as the 520.8 nm.

Calculation of the longest wavelength:

Since

Wavelength = 395 nm = $395\times 10^{-9} m$

Also,

1nm = $10^{-9} m$

And, Maximum kinetic energy = 0.76 eV =$0.76\times 1.6\times 10^{-19} V$

1e = $1.6\times 10^{-19} C$

Now we know that

$hv = \frac{hc}{ \lambda_0} + K_{max}$

Here

$c = 3\times 10^8 m/s$

Now

$h = 6.625\times 10^{-34}$

So,

$6.25\times 10^{-34} \times \frac{3\times 10^8}{395\times 10^{-9)}} = \frac{6.625\times 10^-34*3\times 10^8}{ \lambda _0} + (0.76 \times 1.6 \times 10^{-19})\\\\6.625 \times 10^{-34} \times \frac{3\times 10^{8}}{395 \times 10^{-9}} - 0.76 \times 1.6 \times 10^{-19} = \frac{6.625\times 10^-34*3\times 10^8}{ \lambda _0}$

$\lambda _0 = \frac{6.625\times 10^-34*3\times 10^8}{6.625 \times 10^{-34} \times \frac{3\times 10^8}{395 \times 10^{-9}} - 0.76 \times 1.6 \times 10^{-19} }\\\\= 5.208 \times 10^{-7} m$

= 520.8 nm

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