Answer

Verified

78.9k+ views

Hint: In this question use the concept that the total energy (T.E) is the sum of kinetic energy (K) and the potential energy (U), that is T.E = K + U. Then use the relation that kinetic energy (K) is the modulus of the total energy (T.E) and potential energy (U) is the double of the total energy (T.E) such that the total energy which is the sum of kinetic energy and potential energy is the same. This will help approaching the problem statement.

Given data:

Total energy of an electron in an excited state of hydrogen atom is -3.4eV

Now we have to find out the kinetic and potential energy of electrons in this state.

As we know that the total energy (T.E) is the sum of kinetic energy (K) and the potential energy (U)

Therefore, T.E = K + U

Now as we know that kinetic energy (K) is the modulus of the total energy (T.E).

$ \Rightarrow K = \left| {T.E} \right|$= |-3.4| = 3.4eV

As modulus of any negative quantity is positive.

And the potential energy (U) is the double of the total energy (T.E) so that the total energy which is the sum of kinetic energy and potential energy is the same.

$ \Rightarrow U = 2\left( {T.E} \right)$ = 2(-3.4) = -6.8eV

So the total energy, T.E = K + U = 3.4 + (-6.8) = -3.4eV which is the same as the above total energy.

So kinetic energy of electron in this state is, K = 3.4eV

And potential energy of electron in this state is, U = -6.8eV

So this is the required answer.

Hence option (B) is the correct answer.

Note – In quantum mechanics excited state can be considered as any quantum state that is at higher energy level from the ground. The ground state basically depicts the lowest energy levels that an atom can have.

__Complete step-by-step solution__-Given data:

Total energy of an electron in an excited state of hydrogen atom is -3.4eV

Now we have to find out the kinetic and potential energy of electrons in this state.

As we know that the total energy (T.E) is the sum of kinetic energy (K) and the potential energy (U)

Therefore, T.E = K + U

Now as we know that kinetic energy (K) is the modulus of the total energy (T.E).

$ \Rightarrow K = \left| {T.E} \right|$= |-3.4| = 3.4eV

As modulus of any negative quantity is positive.

And the potential energy (U) is the double of the total energy (T.E) so that the total energy which is the sum of kinetic energy and potential energy is the same.

$ \Rightarrow U = 2\left( {T.E} \right)$ = 2(-3.4) = -6.8eV

So the total energy, T.E = K + U = 3.4 + (-6.8) = -3.4eV which is the same as the above total energy.

So kinetic energy of electron in this state is, K = 3.4eV

And potential energy of electron in this state is, U = -6.8eV

So this is the required answer.

Hence option (B) is the correct answer.

Note – In quantum mechanics excited state can be considered as any quantum state that is at higher energy level from the ground. The ground state basically depicts the lowest energy levels that an atom can have.

Recently Updated Pages

Name the scale on which the destructive energy of an class 11 physics JEE_Main

Write an article on the need and importance of sports class 10 english JEE_Main

Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main

Choose the one which best expresses the meaning of class 9 english JEE_Main

What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main

A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main

Other Pages

Choose the correct statements A A dimensionally correct class 11 physics JEE_Main

The IUPAC name of the following compound is A Propane123tricarbonitrile class 12 chemistry JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

If a wire of resistance R is stretched to double of class 12 physics JEE_Main