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A parallel beam, of light of wavelength 100 nm passed through a sample of atomic hydrogen gas in ground state. (a) Assume that when a phton supplies s

Monjur Alahi

A parallel beam, of light of wavelength 100 nm passed through a sample of atomic hydrogen gas in ground state.
(a) Assume that when a phton supplies some of its energy to a hydrogen atom, the rest of the energy appears an another photon moving in the same direction as the incident photon. Neglecting the light emitted by the excited hydrogen atoms in the direction of the incident beam, what wavelengths may be observed in the transmitted beam?
(b) A radition detector is placed near the gas to detect radiation coming perpendicular to the incident beam. Find the wavelength of radiation that may be detected by the detector.


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1 Answers

Salim Ahmed Kawsar

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Correct Answer - `[(a) 100nm, 560 nm, 3880 m; (b) 103nm, 121 nm, 654 nm]`

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Prove that `^100 C_2^(100)C_2+^(100)C_2^(100)C_4+^(100)C_4^(100)C_6++^(100)C_(98)^(100)C_(100)=1/2[^(200)C_(98)-^(100)C_(49)]dot`

To find `S = .^(100)C_(0).^(100)C_(2)+.^(100)C_(2).^(100)C_(4)+.^(100)C_(4).^(100)C_(6)+"....."+.^(100)C_(98).^(100)C_(100)` Consider, `.^(100)C_(0).^(100)C_(2)+.^(100)C_(1).^(100)C_(3) + .^(100)C_(2).^(100)C_(4)+.^(100)C_(3)+.^(100)C_(5)+"...." + .^(100)C_(98).^(100)C_(100)` `= .^(100)C_(0).^(100)C_(98)+.^(100)C_(1).^(100)C_(97) + .^(100)C_(2).^(100)C_(96)+.^(100)C_(3).^(100)C_(95) + "....."+^(100)C_(98) .^(100)C_(0)` = Coefficients of `x^(98)` in `(1+x)^(100) (1+x)^(100)` `= .^(200)C_(98) " "(1)` Also,...

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