QJEEM19Ch17e0: JEE Main 2019 Chemistry - Class 11 JEEM19Ch17e0 Solution: If the de Broglie wavelength of the electron in n th Bohr orbit …

Question

Verified Solution • 2025–26 Session moderate

If the de Broglie wavelength of the electron in n^th Bohr orbit in a hydrogenic atom is equal to 1.5

\pi

a₀ (a₀ is Bohr radius), then the value of n/z is -

Accepted Answer

According to debroglie hypothesis,

2

\pi

r_n = n

\lambda

\therefore

\lambda

=

{{2\pi {r_n}} \over n}

According to the question,

{{2\pi {r_n}} \over n}

= 1.5

\pi

a₀

We know,

r_n = 0.529

{{{n^2}} \over Z}

= a₀

\times

{{{n^2}} \over Z}

\therefore

{{2\pi } \over n} \times {{{a_0}{n^2}} \over Z}

= 1.5

\pi

a₀

\Rightarrow

{n \over Z}

= 0.75

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