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Dual Nature of Radiation and Matter

Energy in bohr orbit

Suppose an electron is attracted towards the origin by a force

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Suppose an electron is attracted towards the origin by a force $k / r$ , where $k$ is a constant and $r$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n$ th orbital of the electron is found to be $r_{n}$ and the kinetic energy of the electron to be $T_{n}$ . Then, which of the following is true?
(a) $T_{n} \propto \frac{1}{n ^{2}}, r_{n} \propto n^{2}$
(b) $T_{n}$ is independent of
(c) $T_{n} \propto \frac{1}{n}, r_{n} \propto n$
(d) $T_{n} \propto \frac{1}{n}, r_{n} \propto n^{2}$

Name: Video solution 1: Suppose an electron is attracted towards the origin by a force k/r, where k is a constant and r is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn. Then, which of the following is true?(a) Tn∝n21,rn∝n2(b) Tn is independent of(c) Tn∝n1,rn∝n(d) Tn∝n1,rn∝n2
Uploaded: 2023-03-04T12:28:12.000Z
Duration: 7 min

Views: 5,632 students

Updated on: Mar 4, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2008

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Scarlett Discussed

Suppose an electron is attracted towards the origin by a force

k / r

, where

k

is a constant and

r

is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the

n

th orbital of the electron is found to be

r_{n}

and the kinetic energy of the electron to be

T_{n}

. Then, which of the following is true?
(a)

T_{n} \propto \frac{1}{n ^{2}}, r_{n} \propto n^{2}

(b)

T_{n}

is independent of
(c)

T_{n} \propto \frac{1}{n}, r_{n} \propto n

(d)

T_{n} \propto \frac{1}{n}, r_{n} \propto n^{2}

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Exp. (b)

\frac{m v ^{2}}{r _{n}} = \frac{k}{r _{n}}

[given]

m v r_{n} = \frac{nh}{2 π}

[from Bohr's theory]
On solving,

r_{n} \propto n

and

T_{n}

is independent of

n

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Question Text	Suppose an electron is attracted towards the origin by a force $k / r$ , where $k$ is a constant and $r$ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n$ th orbital of the electron is found to be $r_{n}$ and the kinetic energy of the electron to be $T_{n}$ . Then, which of the following is true? (a) $T_{n} \propto \frac{1}{n ^{2}}, r_{n} \propto n^{2}$ (b) $T_{n}$ is independent of (c) $T_{n} \propto \frac{1}{n}, r_{n} \propto n$ (d) $T_{n} \propto \frac{1}{n}, r_{n} \propto n^{2}$
Updated On	Mar 4, 2023
Topic	Dual Nature of Radiation and Matter
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 2
Upvotes	229
Avg. Video Duration	7 min

Text solutionVerified

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