Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced 2012Paper 1
Exam
JEE Advanced
Year
2012
Paper
Paper 1
Subject
Chemistry
Chapter
Structure of Atom

JEE Advanced 2012 · Paper 1 · Chemistry · Structure of Atom

The kinetic energy of an electron in the second Bohr orbit of a...

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0\left[a_{0}\right. is Bohr radius ]::

Options

  1. Ah24π2ma02\frac{h^{2}}{4 \pi^{2} m a_{0}^{2}}
  2. Bh216π2ma02\frac{h^{2}}{16 \pi^{2} m a_{0}^{2}}
  3. Ch232π2ma02\frac{h^{2}}{32 \pi^{2} m a_{0}^{2}}
  4. Dh264π2ma02\frac{h^{2}}{64 \pi^{2} m a_{0}^{2}}

Correct answer

C. h232π2ma02\frac{h^{2}}{32 \pi^{2} m a_{0}^{2}}

Step-by-step solution

As per Bohr's postulate, mvr=nh2π So, v=nh2πmrKE=12mv2 So, KE=12m(nh2πmr)2\begin{array}{l} m v r=\frac{n h}{2 \pi} \quad \text{ So, } v=\frac{n h}{2 \pi m r} \\ \mathrm{KE}=\frac{1}{2} m v^{2} \quad \text{ So, } \mathrm{KE}=\frac{1}{2} m\left(\frac{n h}{2 \pi m r}\right)^{2} \end{array}  Since, r=ao×n2z\text{ Since, } r=\frac{a_{\mathrm{o}} \times n^{2}}{z} So, for 2nd 2^{\text{nd }} Bohr orbit r=ao×221=4aoKE=12m(22h24π2m2×(4ao)2)=h232π2mao2\begin{array}{l} r=\frac{a_{\mathrm{o}} \times 2^{2}}{1}=4 a_{\mathrm{o}} \\ \mathrm{KE}=\frac{1}{2} m\left(\frac{2^{2} h^{2}}{4 \pi^{2} m^{2} \times\left(4 a_{\mathrm{o}}\right)^{2}}\right)=\frac{h^{2}}{32 \pi^{2} m a_{\mathrm{o}}^{2}} \end{array}
Practice Structure of Atom on Quantrex Academy →

More from Structure of Atom

The 2s and the 2p orbital energies of hydrogen atom are E_ 2s (H) and E_ 2p (H)… JEE Advanced 2026X^ a+ and Y^ b+ are hydrogen-like species. The wavelength of light absorbed during the… JEE Advanced 2026Consider two radiations of wavelengths 1. λ_1 = 2000 Å 2. λ_2 = 6000 Å The ratio of the… JEE Main 2026The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary… JEE Main 2026If shortest wavelength of hydrogen atom in Lyman series is x , then longest wavelength in… JEE Main 2026Match the LIST-I with LIST-II List-I Orbital List-II Radial nodes and nodal plane A. 2s… JEE Main 2026Which of the following statement(s) is/are true ? A. If two orbitals have the same value… JEE Main 2026Arrange the following atomic orbitals of multi electron atoms in order of increasing… JEE Main 2026 Full Structure of Atom list All JEE Advanced PYQs