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  • Light of wavelength  ejects photo electrons from a plate

Light of wavelength 1800 \mathrm{~A}^{\circ} ejects photo electrons from a plate of a metal whose work function is  2 \mathrm{eV} . If a uniform magnetic field of  5 \times 10^{-5} T  is applied parallel to plate, what around be the radius of path followed by electrons ejected normally from the plates with maximum energy.

Option: 1

0.10m


Option: 2

0.12m


Option: 3

0.15m


Option: 4

0.18m


Answers (1)

best_answer

The energy of incident photons in eV is given as  E=\frac{12432}{1800} \mathrm{eV}

As the work function of the metal is  2 \mathrm{eV} 

The maximum kinetic energy of the ejected electron is

K \cdot E_{\text {max }}=E-\phi

=6.9-2 \mathrm{eV}=4.9 \mathrm{eV}

If  V_{\text {max }}  be the speed of the fastest electron then we have

 \frac{1}{2} m v_{\text {max }}^2=4 .9 \times 1.6 \times 10^{-19} \mathrm{~J}

\Rightarrow v_{\text {max }}=\frac{\sqrt{2 \times 4.9 \times 1.6 \times 10^{-19}}}{9.1 \times 10^{-31}}=1.31 \times 10^6 \mathrm{~m} / \mathrm{s}

when an electron with this speed enters a uniform magnetic field normally it follows a circular path whose radius is given by
r=\frac{m v}{q B}=\frac{9.1 \times 10^{-31} \times 1.31 \times 10^6}{1.6 \times 10^{-19} \times 5 \times 10^{-5}}=0.150 \mathrm{~m} .

 

Posted by

Deependra Verma

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