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JEE Advanced 2011Paper 2
Exam
JEE Advanced
Year
2011
Paper
Paper 2
Subject
Physics
Chapter
Dual Nature of Matter

JEE Advanced 2011 · Paper 2 · Physics · Dual Nature of Matter

A silver sphere of radius 1 ~cm and work function 4.7 eV is...

A silver sphere of radius 1 cm1 \mathrm{~cm} and work function 4.7eV4.7 \mathrm{eV} is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm200 \mathrm{~nm} wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is A×10ZA \times 10^Z (where 1<A<101 < A < 10 ). The value of ZZ is

Correct answer

0

Step-by-step solution

Photoemission will stop when potential on silver sphere becomes equal to the stopping potential. ∴hcλ−W=eV0\therefore \quad \frac{h c}{\lambda}-W=e V_0 Here, V0=14πε0ner\quad V_0=\frac{1}{4 \pi \varepsilon_0} \frac{n e}{r}∴(12401200eV)−(4.7eV)=9×109×n×1.6×10−1910−2(6.2−4.7)=9×109×n×1.6×10−1910−2 or \quadn=1.5×10−29×1.6×10−10=1.04×107\begin{aligned}& \therefore \quad\left(\frac{1240}{1200} \mathrm{eV}\right)-(4.7 \mathrm{eV})\\ &=\frac{9 \times 10^9 \times n \times 1.6 \times 10^{-19}}{10^{-2}}\\ &(6.2-4.7)=\frac{9 \times 10^9 \times n \times 1.6 \times 10^{-19}}{10^{-2}}\\ & \text{ or } \quadn= \frac{1.5 \times 10^{-2}}{9 \times 1.6 \times 10^{-10}}=1.04 \times10^7 \end{aligned}\thereforeAnsweris7.AnalysisofQuestion(i)Questionismoderatelydifficult.(ii)InAnswer is 7 . Analysis of Question (i) Question is moderately difficult. (ii) In\mathrm{eV}_0ifwesubstitutethevalueofif we substitute the value ofe=1.6 \times 10^{-19} \mathrm{C},thenanswerisinJ.Ifweleaveitthen,answerisin, then answer is in J. If we leave it then, answer is ine \mathrm{~V}.
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