1e:I[80107,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 1f:I[76763,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 21:I[96770,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 22:I[7924,["/_next/static/chunks/235ad55241b6443f.js","/_next/static/chunks/8337ab1f037b6654.js","/_next/static/chunks/c9e933b5fd1a0afc.js","/_next/static/chunks/848a330faa2461ac.js","/_next/static/chunks/9f2942e368a262d2.js","/_next/static/chunks/92f9e11244990470.js","/_next/static/chunks/a8b867fbb1dfca1a.js","/_next/static/chunks/1100f0390a901fa7.js","/_next/static/chunks/bbe6bd9d3c7b0355.js","/_next/static/chunks/a82195c3e5de7dd4.js"],"default"] 1d:T41b,{"@context":"https://schema.org","@graph":[{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://www.divinejee.com"},{"@type":"ListItem","position":4,"name":"The deBroglies wavelength of an electron in the 4 th orbit i","item":"https://www.divinejee.com/question/the-debroglies-wavelength-of-an-electron-in-the-4-th-orbit-is-pi-a0-a0-bohrs-radius"}]},{"@type":"QAPage","mainEntity":{"@type":"Question","name":"Question The deBroglies wavelength of an electron in the 4 th orbit i on Topic","text":"

The de-Broglie's wavelength of an electron in the $4^{\\text {th }}$ orbit is ________ $\\pi \\mathrm{a}_0$. ($\\mathrm{a}_0=$ Bohr's radius)

...","answerCount":1,"upvoteCount":0,"datePublished":"2026-01-16","author":{"@type":"Organization","name":"DivineJEE"},"acceptedAnswer":{"@type":"Answer","text":"Check the detailed solution on the page.","upvoteCount":0,"url":"https://www.divinejee.com/question/the-debroglies-wavelength-of-an-electron-in-the-4-th-orbit-is-pi-a0-a0-bohrs-radius"}}}]}20:T4f7,

The de-Broglie wavelength of an electron can be expressed through its relationship with the principal quantum number $$n$$ in a Bohr orbit. According to de Broglie, the wavelength $ \lambda $ of an electron moving in an orbit can be related to its momentum. However, when considering an electron in an atom, specifically within the Bohr model, we can relate the de-Broglie wavelength to the circumference of the orbit it moves in. The formula representing the de Broglie wavelength of an electron in the $n^{\text{th}}$ orbit of a hydrogen-like atom is:

$$ \lambda_n = \frac{2 \pi r_n}{n} $$

where

$ \lambda_n $ is the de-Broglie wavelength of the electron in the $n^{\text{th}}$ orbit,
$ r_n $ is the radius of the $n^{\text{th}}$ orbit,
$ n $ is the principal quantum number (which is 4 in this case).

According to Bohr's theory, the radius of the $n^{\text{th}}$ orbit is given by:

$$ r_n = n^2 a_0 $$

where $ a_0 $ is the Bohr radius.

For the $4^{\text{th}}$ orbit, $n = 4$, so the radius is:

$$ r_4 = 4^2 a_0 = 16 a_0 $$

Substituting $ r_4 $ into the de-Broglie wavelength formula, we get: