Scribd
Upload
51 views1 page

Atom Difficult Ques

The document discusses the Bohr model of the hydrogen atom, specifically focusing on the effects of replacing the electron with a muon. It calculates the first Bohr radius and ground state energy, concluding that the correct values are 2.56 × 10^-13 m and -2.8 keV, respectively. The document also includes a hint for solving the problem and provides options for the answer.

Uploaded by

Nikhilesh Dolai
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
51 views1 page

Atom Difficult Ques

The document discusses the Bohr model of the hydrogen atom, specifically focusing on the effects of replacing the electron with a muon. It calculates the first Bohr radius and ground state energy, concluding that the correct values are 2.56 × 10^-13 m and -2.8 keV, respectively. The document also includes a hint for solving the problem and provides options for the answer.

Uploaded by

Nikhilesh Dolai
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

Result Analysis Summary

Question 12 of 32 | Bohr's Model of Atom | Q4 - Q20

The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals 0.5 A
˚
and its ground state energy equals
−13.6 eV. If the electron in the hydrogen atom is replaced by a muon (μ )[charge same as electron and mass 207 m ], the first Bohr
−
e

radius and ground state energy will be:


( m represents the mass of an electron)
e

1. m, eV
−13
0.53 × 10 − 3.6

2. 25.6 × 10
−13
m, − 2.8 eV

3. 2.56 × 10
−13
m, − 2.8 keV

4. 2.56 × 10
−13
m, − 13.6 eV

We see that you have not attempted question, Please mention reason from below.

Conceptual Mistake Not Studied or Forgotten

Show Me in NCERT

Show Me in Video

Explanation:
Hint: r
2 2
n h
=
2 2
4π mkze

Step: Find the first Bohr radius and ground state energy.
The reduced mass is given by;
mM
μ =
m+M

The Bohr radius is given by;


2 2
n h
r =
2 2
4π mkze

The reduced mass is written as;


me Mnucleus

μ =
me +Mnucleus

207me ×1836me
⇒ μ =
207me +1836me

⇒ μ = 186me

The radius of the first orbit is written as;


me
r1 = × 0.51
186me

−13
⇒ r1 = 2.56 × 10 m

and energy of the first Bohr is written as;


μ
E1 = E
m
186me
⇒ E1 = × (−13.6)
me

⇒ E1 = −2.8 keV

Hence, option (3) is the correct answer.

1x 00:00

(1) 12% (2) 14%

(3) 51% (4) 25%

You might also like