Single Choice

The wavelength of third line of the Balmer series for a H atom is:

A21/100R
B100/21R
Correct Answer
C21R/100
D100R/21

Solution

Balmer series $$\Rightarrow {n}_{1}=2$$

The third line of Balmer series $$\Rightarrow {n}_{2}=5$$

Rydberg equation $$\Rightarrow \cfrac {1} {\lambda}= {Rz}^{2} \left[ \cfrac {1} {{n}_{1}^{2}} - \cfrac {1} {{n}_{2}^{2}} \right]$$

$$\Rightarrow \cfrac {1}{\lambda } = \left( 10967800 \right) \left(1 \right)^{2} $$

$$\left[ \cfrac { 1 }{ { { 2 }^{ 2 } }} -\cfrac { 1 }{ { 5 }^{ 2 } } \right] $$

$$ \cfrac {1}{\lambda }= \cfrac {21} {100}R$$
Wavelength of $${3}^{rd}$$ line of Balmer, $$ \lambda = \cfrac {100} {21R}$$

So, the correct option is $$B$$

SIMILAR QUESTIONS

Atomic Structure

For given energy of photon, $$E=3.03\times 10^{-19}J$$ corresponding wavelength will be: $$(h=6.6\times { 10 }^{ -34} sec$$, $$C=3\times { 10 }^{ 8 }m/sec.)$$

Atomic Structure

Calculate the wavelength associated with an electron moving with a velocity of $${ 10 }^{ 10 } cm$$ per sec.

Atomic Structure

What should be the mass of the photon of sodium if its wavelength is $$5894 \mathring { A }$$. The velocity of light is $$3\times { 10 }^{ 8 }\ { metre }/{ second }$$ and the value of h is $$6.6252 \times { 10 }^{ -34 } kg\ { { m }^{ 2 } }/{ s\ }?$$

Atomic Structure

A near UV photon of $$300\ nm$$ is absorbed by a gas and then re-emitted as two photons. One photon is red light with wavelength $$760\ nm$$, then the wavelength of the second photon is:

Atomic Structure

The energy of a photon is given as $$3.03\times 10^{-19}$$ J/atom. The wavelength of the photon is :

Atomic Structure

The energy difference between the ground state of an atom and its excited state is $$3\times 10^{-19}J$$. What is the wavelength of the photon required for this transition?

Atomic Structure

A body of mass 10g is moving with a velocity of 100 $$ms^{-1}$$. The wavelength associated with it is :

Atomic Structure

The wavelength of an electron moving with velocity of $$10^7ms^{-1}$$ is:

Atomic Structure

What will be the wavelength of an electron moving with $$\frac{1}{10}th$$ of velocity of light?

Atomic Structure

If travelling at same speeds, which of the following matter waves have the shortest wavelength?

Contact Details