If the de Brogile wavelength of the electron in $\mathrm{n}^{\text {th }}$ Bohr orbit in a hydrogenic atom is equal to $1.5 \pi \mathrm{a}_{0}$ ( $\mathrm{a}_{0}$ is Bohr radius), then the value of $\mathrm{n} / \mathrm{z}$ is :

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Atomic Structure

If the de Brogile wavelength of the electron in

n^{th}

Bohr orbit in a hydrogenic atom is equal to

1.5 π a_{0}

(

a_{0}

is Bohr radius), then the value of

n / z

is :

Answer: (D)

Bohr's condition sets the orbit circumference equal to a whole number of de Broglie wavelengths,

2 π r = nλ

. With

r = \frac{n ^{2} a _{0}}{z}

this gives

λ = \frac{2 π n a _{0}}{z}

. Setting

λ = 1.5 π a_{0}

\frac{2 π n a _{0}}{z} = 1.5 π a_{0}

, so

\frac{n}{z} = \frac{1.5}{2} = 0.75

JEE Main · 2019 · 12 Jan 2019 · Shift 2 · Single correct option