**Problem and solution**

When the electron in hydrogen atom jumps from second orbit to
first orbit, a certain wavelength is emitted. When the electron jumps from the
third orbit to first orbit, what is the new wavelength emitted in terms of the
first wavelength?

We can solve this problem basing on the derivation is that we
made for the reciprocal of the wavelength in terms of the Redberg constant. By
applying the given condition in the problem in two different equations and by
simplifying them we can solve the problem as shown below.

**Problem and solution**

What is the ratio of largest to shortest wavelengths in the
Balmer series of the hydrogen spectrum?

We can solve this problem also basing on the derivation that
we made for the reciprocal of the wavelength in terms of principal quantum
numbers. For the wavelength to be maximum, the corresponding energy has to be
minimum. It is possible only when the electronic jumping from the third orbit
to second orbit.

Further wavelength to be minimum, the corresponding energy
has to be maximum. This is possible when their electron is jumping from
infinite orbit to second orbit. The corresponding equation is written in the
problem is solved as shown below.

**Problem and solution**

In a hydrogen atom electron is jumped from the fifth orbit to
first orbit. What is the recoil speed of the hydrogen atom in this process?

As the electronic jumping from higher orbit to lawyer orbit,
there is some emission of energy. This emitted energy will have a certain
wavelength. To compensate the jerk that is generated by this emitted energy,
nuclear is most with a little bit velocity and here we are going to calculate
that velocity. By substituting the wavelength that we have derived in the de
Broglie concept we can derive the equation for the velocity of the nucleus as
shown below.

**Problem and solution**

If the wavelength of the first member of the Balmer series in
the hydrogen spectrum is 6564 Å, what will be the wavelength of the second
member of the Balmer series?

We can solve this problem by writing the equation for the
reciprocal of the wavelength using the atomic model. By comparing the given two
conditions we can get the answer as shown below.

**Problem and solution**

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Dual Nature of Radiation and Matter complete lesson

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