
The electron in a hydrogen atom makes a transition , where and are the principal quantum numbers of the two energy states. Assume Bohr's model to be valid. The time period of the electron in the initial state is eight times that in the final state. What are the possible values of and ?
Answer
411k+ views
Hint:Before calculating the and values, you should know the relation between time period and orbit of the electron. We all know the time period is equal to the revolution taking per frequency. So we can use this relation to obtain the values of and .
Formula used:
Where, - is the time period,
-frequency
-number of orbitals
Complete step by step solution:
The period for the th orbitals electron is written as,
The period for the th orbitals electron is written as,
Hence, divide the two time period, we get
The time period for orbital is times greater than the orbital. So we can write the relation as,
,
Substitute the relation into the equation means, we can get,
The possible values of and are, , , and so on.
Note: From Bohr's model of the hydrogen atom, easily calculate the time period taken to complete the one rotation of the electron. The time period is calculated from the simple formula, the time period is equal to the total distance covered divided by the velocity of the electron. From this formula also we can easily calculate the time period of Bohr's orbit. The time it takes to complete one rotation to the electron is seconds.
Formula used:
Where,
Complete step by step solution:
The period for the
The period for the
Hence, divide the two time period, we get
The time period for
Substitute the relation into the equation means, we can get,
The possible values of
Note: From Bohr's model of the hydrogen atom, easily calculate the time period taken to complete the one rotation of the electron. The time period is calculated from the simple formula, the time period is equal to the total distance covered divided by the velocity of the electron. From this formula also we can easily calculate the time period of Bohr's orbit. The time it takes to complete one rotation to the electron is
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
A deep narrow valley with steep sides formed as a result class 12 biology CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Which are the Top 10 Largest Countries of the World?

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Derive an expression for electric potential at point class 12 physics CBSE
