Share
Notifications

View all notifications
Advertisement

# Obtain an Expression for the Radius of Bohr Orbit for H-atom. - Physics

Login
Create free account

Forgot password?

#### Question

Obtain an expression for the radius of Bohr orbit for H-atom.

#### Solution

Let us consider an electron revolving around the nucleus in a circular orbit of radius ‘r’.

According to Bohr’s first postulate, the centripetal force is equal to the electrostatic force of attraction. That is

"mv"^2/"r"=1/(4piepsilon_o)xx"e"^2/"r"^2

"Or,""v"^2="e"^2/(4piepsilon_o"mr") -------------------(1)

According to the Bohr's second postulate:

"Angular momentum"= "n""h"/(2pi)

"mvr"="n""h"/(2pi)

Or,                   "v"="nh"/(2pi"mr") -----------------(2)

Or,                   "v"^2=("n"^2"h"^2)/(4pi^2"m"^2"r"^2) ---------------------(3)

Comparing eqn (1) and eqn (3), we get

"e"^2/(4piepsilon_o"mr")=("n"^2"h"^2)/(4pi^2"m"^2"r"^2)

"Or,""r"=(("h"^2epsilon_o)/(pi"me"^2))"n"^2 ----------------------(4)

This equation gives the radius of the nth Bohr orbit.

"For n"=1,"r"_1=(("h"^2epsilon_o)/(pi"me"^2))=0.537" ---------------(5)"

"In general,"" r"_n=(("h"^2epsilon_o)/(pi"me"^2))"n"^2

The above equation gives the radius of Bohr orbit.

Is there an error in this question or solution?
Advertisement

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 7.1 | 3.00 marks
Advertisement

#### Video TutorialsVIEW ALL [2]

Solution Obtain an Expression for the Radius of Bohr Orbit for H-atom. Concept: Bohr'S Model for Hydrogen Atom.
Advertisement