#
ENERGY AND WAVELENGTH OF PHOTON

IIT JEE - NEET

## A gas absorbs a photon of 355 nm and emits at two wavelengths. If one of the emissions is at 680 nm, the other is at :

(AIEEE 2010)

a) 325 nm

b) 743 nm

c) 518 nm

d) 1035 nm

**Logic:**

Since energy is conserved, the energy, E_{abs} of absorbed photon is equal to total of energies, (E_{1}+ E_{2}) of two photons emitted.

i.e. E_{abs} = E_{1}+ E_{2}

Where:

E_{1} = Energy of first photon emitted

E_{2} = Energy of second photon emitted

Energy, E and wavelength, λ of a photon are related as follows:

E = hc/λ

Where:

h = Planck's constant

c = velocity of light (a constant)

Therefore:

1/λ_{abs} = 1/λ_{1} + 1/λ_{2}

**Solution:**

Upon substituting the known values in above equation:

1/355 = 1/680 + 1/λ_{2}

By solving above equation:

λ_{2} = 742.76 nm

Conclusion:

Correct option is "b".

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## Related questions

### 1) The energy of a photon is 3 x 10^{-12} erg. What is the wavelength in nm?

#### (Eamcet - 2006-E)

a) 662

b) 1324

c) 66.2

d) 6.62

Solution:

We know that:

E = hc/λ

or

λ= hc/E

Therefore:

wavelength λ = hc/E = 6.626 x 10^{-27} erg s x 3.0 x 10^{10 }cm s^{-1} / 3 x 10^{-12} erg = 6.626 x 10^{-}^{5} cm

Now:

1 cm = 10^{7} nm

Therefore the wavelength in nm = 6.626 x 10^{-}^{5} x 10^{7 }nm = 6.626 x 10^{2} nm = 662.

#### 2) The ratio of the energy of a photon of 2000 Å wavelength radiation to that of 4000 Å radiation is :

#### (IIT JEE 1986)

a) 1/4

b) 4

c) 1/2

d) 2

Solution:

From

E = hc/λ

The ratio of energies of two radiations is given by:

E_{1}/E_{2} = λ_{2}/λ_{1} = 4000/2000 = 2

Note: Energy is inversely proportional to wavelength.

### 2) Which one of the following frequencies of radiation (in Hz) has a wavelength of 600 nm?

#### (EAMCET 2011-M)

a) 5.0 x 10^{14}

b) 2.0 x 10^{13}

c) 5.0 x 10^{16}

d) 2.0 x 10^{14}

Solution:

c = νλ

where

ν = frequency

λ = wavelength

c = velocity of light

Therefore:

ν = c / λ = 3.0 x 10^{8} m s^{-1} / 600 x 10^{-9} m = 5.0 x 10^{14} s^{-1} = 5.0 x 10^{14} Hz

## Homework

1) If the wavelength of an electromagnetic radiation is 2000 Å , what is the energy in ergs?

2) What is the wavenumber of electromagnetic radiation that has a wavelength 3 x 10^{-8} cm?

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