LASER * Usefulness of Einstein’s coefficients in construction of laser : (1) The rate of stimulated emission must be as large as possible compared to the rate of spontaneous emission. i.e (𝑹𝟐𝟏)𝒔𝒑 (𝑹𝟐𝟏)𝒔𝒕 < < 1 Now , (𝑹𝟐𝟏)𝒔𝒑 (𝑹𝟐𝟏)𝒔𝒕 = 𝑨𝟐𝟏 𝑵𝟐 𝑩𝟐𝟏 𝑵𝟐 𝝆 ( 𝝂 ) = 𝒄 𝟑 𝟖 𝝅 𝒉 𝒇 𝟑 [ 𝒆 𝒉 𝒇 𝑲 𝑻 − 𝟏] 𝟖 𝝅 𝒉 𝒇 𝟑 𝒄 𝟑 ∴ (𝑹𝟐𝟏)𝒔𝒑 (𝑹𝟐𝟏)𝒔𝒕 = 𝒆 𝒉 𝒇 𝑲 𝑻 − 𝟏 Thus, from the above eqn. we can see that at normal temperature the value of frequency ( f ) must be small . (2) The ratio of the rate of stimulated emission to the rate of absorption should be as large as possible . i.e (𝑹𝟐𝟏)𝒔𝒕 (𝑹𝟏𝟐)𝒂𝒃 ≥ 𝟏 ∴ (𝑹𝟐𝟏)𝒔𝒕 (𝑹𝟏𝟐)𝒂𝒃 = 𝑩𝟐𝟏 𝑵𝟐 𝝆 ( 𝝂 ) 𝑩𝟏𝟐 𝑵𝟏 𝝆 ( 𝝂 ) = 𝑵𝟐 𝑵𝟏 ( 𝑩𝟐𝟏 𝑩𝟏𝟐 = 𝟏 ) ∴ (𝑹𝟐𝟏)𝒔𝒕 (𝑹𝟏𝟐)𝒂𝒃 = 𝒆 − 𝒉 𝒇 𝑲 𝑻 From the above equation we can conclude tha...