Question

Find the relation between the three wavelengths from the energy level diagram shown:

Answer 1

Answer:

1/LAMBDA2 -1/LAMBDA3=1/LAMBDA1

Explanation:

FOR LAMBDA3

EA-EC=HC/LAMBDA3

FOR LAMBDA2

EA-EB=HC/LAMBDA2

FOR LAMBDA1

EB-EC=HC/LAMBDA1

SOLVE AND SUBTITUE ALL EQ ABOVE TO GET YOUR ANSWER

Answer 2

The relation between the three wavelengths is $\lambda_{3}=\dfrac{\lambda_{1}\lambda_{2}}{\lambda_{2}+\lambda_{1}}$.

Explanation:

We know that.

The formula of energy is

$E=\dfrac{hc}{\lambda}$

here, E = energy gap between two levels

Where, E = energy

h = Planck constant

c = speed of light

$\lambda$ = wave length

According to figure,

The energy in CB is

$E_{CB}=\dfrac{hc}{\lambda_{1}}$

Here, $E_{CB}$ = energy gap between level C and B

The energy in BA is

$E_{BA}=\dfrac{hc}{\lambda_{2}}$

Here, $E_{BA}$ = energy gap between level B and A

The energy in CA is

$E_{CA}=\dfrac{hc}{\lambda_{3}}$

Here, $E_{CA}$ = energy gap between level C and A

We need to calculate the relation between the wavelength

Using formula of energy

$E_{CA}=E_{CB}+E_{BA}$

Put the value into the formula

$\dfrac{hc}{\lambda_{3}}=\dfrac{hc}{\lambda_{1}}+\dfrac{hc}{\lambda_{2}}$

$\dfrac{1}{\lambda_{3}}=\dfrac{1}{\lambda_{1}}+\dfrac{1}{\lambda_{2}}$

$\lambda_{3}=\dfrac{\lambda_{1}\lambda_{2}}{\lambda_{2}+\lambda_{1}}$

Hence, The relation between the three wavelengths is $\lambda_{3}=\dfrac{\lambda_{1}\lambda_{2}}{\lambda_{2}+\lambda_{1}}$.

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Topic : energy level

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