JEE Mains · Physics · STD 12 - Dual nature of radiation and matter
- JEE Mains 2013
- Hard
- MCQ
A copper ball of radius \(1\, cm\) and work function \(4.47\,eV\) is irradiated with ultraviolet radiation of wavelength \(2500\mathop A\limits^o \). The effect of irradiation results in the emission of electrons from the ball. Further the ball will acquire charge and due to this there will be a finite value of the potential on the ball. The charge acquired by the ball is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(5.5 \times {10^{ - 13}}\,C\)
Step-by-step Solution
Detailed explanation
Let us assume that,
Lost energy of electron is equal to its stopping potential
\(E\, = \,KE\, + \,\Phi \)
\(\frac{12100}{\lambda A}=V+4.47 \mathrm{eV}\)
\(\frac{12100}{2500}=V+4.47\)
\(\frac{124}{25}=V+4.47\)
\(4.95=V+4.47\)
\(\mathrm{V}=4.95-4.47=0.48\)
\(\mathrm{V}_{\text {sphere }}=\frac{K Q}{r}=\frac{9 \times 10^{9} \mathrm{Q}}{100}\)
\(0.48=\frac{9 \times 10^{8} Q}{100}\)
\(Q=\frac{48 \times 10^{9}}{9 \times 100}\)
\(Q=5.5 \times 10^{-13} \mathrm{C}\)
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