Light of wavelength $$180\,nm$$ ejects photoelectron from a plate of a metal whose work function is $$2\,eV.$$ If a uniform magnetic field of $$5 \times {10^{ - 5}}T$$ is applied parallel to plate, what would be the radius of the path followed by electrons ejected normally from the plate with maximum energy?
A.
$$1.239\,m$$
B.
$$0.149\,m$$
C.
$$3.182\,m$$
D.
$$2.33\,m$$
Answer :
$$0.149\,m$$
Solution :
If $${v_{\max }}$$ is the speed of the fastest electron emitted from the metal surface, then
$$\eqalign{
& \frac{{hc}}{\lambda } = {W_0} + \frac{1}{2}mv_{\max }^2 \cr
& \frac{{\left( {6.63 \times {{10}^{ - 34}}} \right) \times \left( {3 \times {{10}^8}} \right)}}{{\left( {180 \times {{10}^{ - 9}}} \right)}} \cr
& = 2 \times \left( {1.6 \times {{10}^{ - 19}}} \right) + \frac{1}{2}\left( {9.1 \times {{10}^{ - 31}}} \right)v_{\max }^2 \cr
& \therefore v = 1.31 \times {10^6}\,m/s \cr} $$
The radius of the electron is given by
$$r = \frac{{mv}}{{qB}} = \frac{{\left( {9.1 \times {{10}^{ - 31}}} \right) \times \left( {1.31 \times {{10}^6}} \right)}}{{\left( {1.6 \times {{10}^{ - 19}}} \right) \times \left( {5 \times {{10}^{ - 9}}} \right)}} = 0.149\,m$$
Releted MCQ Question on Modern Physics >> Dual Nature of Matter and Radiation
Releted Question 1
A particle of mass $$M$$ at rest decays into two particles of
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A proton has kinetic energy $$E = 100\,keV$$ which is equal to that of a photon. The wavelength of photon is $${\lambda _2}$$ and that of proton is $${\lambda _1}.$$ The ration of $$\frac{{{\lambda _2}}}{{{\lambda _1}}}$$ is proportional to