The allowed energy the particle a particular value of n is proportional to -mathrm-a-2-mathrm-a-1-mathrm-a-3-2-mathrm-a-2-

A-n-x3BB-2De broglie wavelength-x3BB-hmvSubsitutep-nh2aE-12mv2-p22m-n2h28a2m

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The allowed energy for the particle for a particular value of n is proportional to :
$a^{- 2}$
$a^{- 1}$
$a^{- 3 / 2}$
$a^{2}$

a^{- 2}

a^{- 3 / 2}

a^{- 1}

a^{2}

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Solution

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$a = \frac{n λ}{2}$
De broglie wavelength
$λ = \frac{h}{m v}$
Subsitute
$p = \frac{n h}{2 a}$
$E = \frac{1}{2} m v^{2} = \frac{p^{2}}{2 m} = \frac{n^{2} h^{2}}{8 a^{2} m}$

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The allowed energy for the particle for a particular value of n is proportional to :

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E = p^{2} / 2 m .

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The allowed energy for the particle for a particular value of n is proportional to :a−2a−1a−3/2a2

a=nλ2De broglie wavelengthλ=hmvSubsitutep=nh2aE=12mv2=p22m=n2h28a2m

The allowed energy for the particle for a particular value of n is proportional to :
$a^{- 2}$
$a^{- 1}$
$a^{- 3 / 2}$
$a^{2}$

$a = \frac{n λ}{2}$
De broglie wavelength
$λ = \frac{h}{m v}$
Subsitute
$p = \frac{n h}{2 a}$
$E = \frac{1}{2} m v^{2} = \frac{p^{2}}{2 m} = \frac{n^{2} h^{2}}{8 a^{2} m}$