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Bohr model
Appears in
Concepts tested here
- Energy levels of hydrogen-like ions
- Orbital speed in hydrogen-like ions
All Questions
2015 AIPMT-I 1 question
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Consider 3rd orbit of $He^+$ (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given K = $9\times 10^9$ constant, Z = 2 and h (Planck's constant) = $6.6\times 10^{-34}$ Js]$v_n = \frac{2\pi KZe^2}{nh} = \left(\frac{Z}{n}\right)\frac{2\pi Ke^2}{h}$
$\frac{2\pi Ke^2}{h} = \frac{2\times 3.14\times 9\times10^9\times(1.6\times10^{-19})^2}{6.6\times10^{-34}} \approx 2.2\times 10^6$ m/s
$v_3 = \frac{2}{3}\times 2.2\times 10^6 = 1.46\times 10^6$ m/s
2010 AIPMT-PRE 1 question
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The energy of a hydrogen atom in the ground state is −13.6 eV. The energy of a $He^+$ ion in the first excited state will beFor a hydrogen-like ion: $E_n = -13.6\frac{Z^2}{n^2}$ eV
For $He^+$, Z = 2; the first excited state is n = 2.
$E_2 = -13.6\times\frac{2^2}{2^2} = -13.6\times\frac{4}{4}$
$E_2 = -13.6$ eV