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Some energy levels of a molecule are shown in fig. The ratio of the wavelengths r=λ1/λ2is given by:


(a) r=13
(b) r=43
(c) r=23
(d) r=34

Answer
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Hint: we have been given two wavelengths and here are the two transitions. So assuming the corresponding two these two transitions, there is the emission of photons in each case. So firstly we will find the energy of that particular photon then using the relation which we have given in the formula, we will find the ratio between these two wavelengths.
Formula used
The energy of photons,
E=hcλ
Here,
E, will be the energy
h, will be the planck's constant
c, will be the speed of light
λ, will be the wavelength

Complete Step By Step Solution: As we know the formula for the energy of the photon and it can be written as
E=hcλ
And from here, λcan be written as
λ=hcE
And hence we can say that
λ1E
Now from the figure,
The energy of a photon of wavelength λ2will be equal to
E2=E(43)
On solving the above equation, we get
E2=E3
Now we will calculate the Energy of the photon of wavelength λ1 and it will equal to
E1=E(2E)
On solving the above equation, we get
E1=E
So now we will calculate the ratios between the two energies
Therefore, it can be written as
λ1λ2=E2E1
Now on substituting the values, we get
λ1λ2=(E3)E
So we will solve the final above equation to get the required ratios
r=λ1λ2=13

Therefore, the option awill be the correct choice.

Note: According to Einstein's equation E=mc2 anything that possesses energy has mass and anything that has mass has energy which is equal to the mass of the particle times square of the speed of light. Photons have 0 rest mass but they have Energy which is equal to Planck constant times its frequency. So, if the photon has a fixed amount of energy which will be more than zero with zero rest mass but the photon does not exist which has 0 moving mass so its energy will be zero.