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JEE Main 20231 FebruaryMorning Shift
Exam
JEE Main
Year
2023
Date
1 February
Shift
Morning Shift
Subject
Physics
Chapter
Atomic Physics

JEE Main 2023 · 1 February · Morning Shift · Physics · Atomic Physics

A light of energy 12 . 75eV is incident on a hydrogen atom in its...

A light of energy 12.75eV12 . 75eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is xπ×10−17eVs\dfrac{x}{\pi} \times {10}^{- 17}eVs. The value of xx is ______ (use h=4.14×10–15eVs,c=3×108ms–1h = 4 . 14 \times {10}^{– 15}eVs, c = 3 \times {10}^{8}m{s}^{– 1})

Correct answer

0

Step-by-step solution

Let the electron jumped to nth{n}^{th} excited state.

In the ground state, energy E=−13.6eVE = - 13 . 6eV

So, using relation 12.75=13.6[112−1n2]12 . 75 = 13 . 6\left[\dfrac{1}{{1}^{2}} - \dfrac{1}{{n}^{2}}\right]

⇒0.9375=[1−1n2]⇒n2=16⇒ 0 . 9375 = \left[1 - \dfrac{1}{{n}^{2}}\right] ⇒ {n}^{2} = 16

⇒n=16=4⇒ n = \sqrt{16} = 4

Now, angular momentum, L=nh2π=4h2π=2hπL = \dfrac{nh}{2\pi} = \dfrac{4h}{2\pi} = \dfrac{2h}{\pi}

=2π×4.14×10−15= \dfrac{2}{\pi} \times 4 . 14 \times {10}^{- 15}

=828×10−17πeVs= \dfrac{828 \times {10}^{- 17}}{\pi}eVs

Hence, the value of x=828x = 828.

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