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QJEEM20Phe7ce: JEE Main 2020 Physics - Class 12 JEEM20Phe7ce Solution: The time period of revolution of electron in its ground state…

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 ×\times 10-16 s. The frequency of revolution of the electron in its first excited state (in s-1) is :

Multiple Choice Options

  • A 5.6 ×\times 1012
  • B 1.6 ×\times 1014
  • C 7.8 ×\times 1014
  • D 6.2 ×\times 1015

Step-by-Step Verified Solution

Time period of revolution of electron in nth orbit

V = 2πrV{{2\pi r} \over V}

= 2πa0(n2Z)V0(Zn){{2\pi {a_0}\left( {{{{n^2}} \over Z}} \right)} \over {{V_0}\left( {{Z \over n}} \right)}}

⇒\Rightarrow T ∝\propto n3Z2{{{{n^3}} \over {{Z^2}}}}

∴\therefore T1T2=n13n23{{{T_1}} \over {{T_2}}} = {{n_1^3} \over {n_2^3}}

⇒\Rightarrow 1.6×10−16T2=1(2)3{{1.6 \times {{10}^{ - 16}}} \over {{T_2}}} = {1 \over {{{\left( 2 \right)}^3}}}

⇒\Rightarrow T2 = 1.6 ×\times 8 ×\times 10-16

∴\therefore f2 = 1T2{1 \over {{T_2}}} = 11.6×8×10−16{1 \over {1.6 \times 8 \times {{10}^{ - 16}}}} = 7.8 ×\times 1014

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