JEE Main 2025 Jan 29 Shift 1, Chemistry Q15: Dual Character Of Matter And Radiation

JEE Main2025Jan 29, Shift 1Chemistry

If $a_{0}$ is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength ( $λ$ ) of the electron present in the second orbit of hydrogen atom? [ $n$ : any integer]

A
$\frac{2 a _{0}}{nπ}$
B
$\frac{8 π a _{0}}{n}$
C
$\frac{4 π a _{0}}{n}$
D
$\frac{4 n}{π a _{0}}$

Solution

The Bohr quantisation condition states that the orbit circumference equals an integral number of de-Broglie wavelengths: $2 π r_{n} = nλ .$

For hydrogen, $r_{n} = n^{2} a_{0}$ , so $r_{2} = 4 a_{0}$ .

Therefore $λ = \frac{2 π ( 4 a _{0} )}{n} = \frac{8 π a _{0}}{n} .$

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JEE Main 2025 Jan 29 Shift 1, Chemistry Q15: Dual Character Of Matter And Radiation

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