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Atoms and Nuclei question

2020 · Shift 1 · Q47

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JEE Advanced
Physics
Atoms and Nuclei
2020 · Shift 1 · Q47

Atoms and Nuclei question

2020 · Shift 1 · Q47

JEE AdvancedPhysicsAtoms and NucleiMultiple correct+4 / −2

A particle of mass m moves in circular orbits with potential energy V(r) = Fr, where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle’s orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the nth orbit (here h is the Planck’s constant)

A
$R \propto {n^{{1 \over 3}}}$ and $v \propto {n^{{2 \over 3}}}$
B
$R \propto {n^{{2 \over 3}}}$ and $v \propto {n^{{1 \over 3}}}$
C
$E = {3 \over 2}{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}$
D
$E = 2{\left( {{{{n^2}{h^2}{F^2}} \over {4{\pi ^2}m}}} \right)^{{1 \over 3}}}$

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