Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Solve! Suppose an electron is attracted towards the origin by a force k / r where k is constant 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 fo

Suppose an electron is attracted towards the origin by a force  k / r where k is constant 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?

  • Option 1)

    T_{n}\alpha \frac{1}{n},r_{n}\alpha\: n^{2}

  • Option 2)

    T_{n}\alpha \frac{1}{n^{2}},r_{n}\alpha\: n^{2}

  • Option 3)

    T_{n}\: Independent \: of \: \: n,\: \: \: r_{n}\alpha\: n

  • Option 4)

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

 

Answers (1)

best_answer

As we learnt in

Bohr quantisation principle -

mvr=\frac{nh}{2\pi } \\2\pi r= n\lambda

- wherein

Angular momentum of an electron in  stationary orbit is quantised.

 

 

Supposing that the force of attraction in Bohr atom does not follow inverse square law but inversely proportional to r ,

\frac{1}{4\pi \varepsilon _{0}}\frac{e^{2}}{r} would have been     = \frac{m\nu ^{2}}{r}

\therefore m\nu ^{2}= \frac{e^{2}}{4\pi \varepsilon _{0}}= k\Rightarrow \frac{1}{2}m\nu ^{2}= \frac{1}{2}k

This is independent of n 

From m\nu r_{n}= \frac{nh}{2\pi }

as\: m\nu \: \: is \: independent \: of\: r,r_{n}\alpha n

Correct option is 3.


Option 1)

T_{n}\alpha \frac{1}{n},r_{n}\alpha\: n^{2}

This is an incorrect option.

Option 2)

T_{n}\alpha \frac{1}{n^{2}},r_{n}\alpha\: n^{2}

This is an incorrect option.

Option 3)

T_{n}\: Independent \: of \: \: n,\: \: \: r_{n}\alpha\: n

This is the correct option.

Option 4)

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

This is an incorrect option.

Posted by

perimeter

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

BTech Admission 2025 Live: JEE Mains, SRMJEEE, MET registrations underway; MHT CET syllabus updates
anam-khan

Centre issues coaching guidelines, prohibits centres from using false claims like '100% selection'
anam-khan

BTech Admissions 2025 Live: JEE Mains, SRMJEE, VITEEE dates out; AEEE, MET registrations underway

Latest Question