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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Physics
Chapter
Dual Nature of Matter

BITSAT 2012 · Physics · Dual Nature of Matter

In an experiment on photoelectric effect photons of wavelength 300...

In an experiment on photoelectric effect photons of wavelength 300nm300 \mathrm{nm} eject electrons from a metal of work function 2.25eV2.25 \mathrm{eV}. A photon of energy equal to that of the most energetic electron corresponds to the following transition in the hydrogen atom:

Options

  1. An=2n=2 to n=1n=1 state
  2. Bn=3n=3 to n=1n=1 state
  3. Cn=3n=3 to n=2n=2 state
  4. Dn=4n=4 to n=3n=3 state

Correct answer

C. n=3n=3 to n=2n=2 state

Step-by-step solution

Given ϕ=2.25eV\phi=2.25 \mathrm{eV} \lambda=300 ×\times100^{-3}  m\mathrm{~m}Energy of the given photon, E=hv=hcλ=663×10−34×3×108300×10−9=\mathrm{E}=\mathrm{hv} =\frac{\mathrm{hc}}{\lambda}=\frac{663 \times 10^{-34} \times 3 \times 10^8}{300 \times 10^{-9}}=6.63 ×\times10^{-19}  J=\mathrm{~J}=4.13 eV\mathrm{eV}Now, E=hcλ−ϕ=\mathrm{E}=\frac{\mathrm{hc}}{\lambda}-\phi=4.137-2.25=1.88 eV→(\mathrm{eV} \rightarrow(1) So, 1.88eV1.88 \mathrm{eV} energy is used to jump from one orbit to another orbit by electron. Therefore, energy of different orbital of hydrogen ⇒n=1234E=−13.6ev−3.4−1.51−0.85\begin{array}{rrrr} \Rightarrow\mathrm{n}=1 & 2 & 3 & 4 \\ \mathrm{E}=-13.6 \mathrm{ev}& -3.4 & -1.51 & -0.85 \end{array}And fromstatement(1),1.18=Ei−Ef{Ei&Ef are  energy  of  initial  and  final  orbit }Andalsofromtheabovetable,wecanobservethat,from statement (1), 1.18=E_i-E_f\left\{E_i \& E_f \quad\right.\text{ are }\text{ energy }\text{ of }\text{ initial }\text{ and }\text{ final }\text{ orbit } \} And also from the above table, we can observe that,E_{\mathrm{i}}-\mathrm{E}_{\mathrm{f}}=(−=(-1.51)-(-3.4)=1.89 eV=E\mathrm{eV} =\mathrm{E}_{2}-\mathrm{E}_{3}$ That the electron jumps from 3rd to 2nd orbit. Therefore, with one photon of 3oonm wavelength hydrogen electron can jump from 3 to 2 .
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