Integral psi_A_mu O~_B_2u psi_A_u d tau in D_2h symmetry Integral psi_A_tau O~_A

Question

Integral psi_A_mu O~_B_2u psi_A_u d tau in D_2h symmetry Integral psi_A_tau O~_A_1 psi_A_2 dtau in C_3v symmetry Integral psi_sigma_g O~_sigma_0 psi_sigma_0 d tau in D_xh symmetry Integral psi_E~ O~_A2_psi_T_1 d tau in T_d symmetry What is the frequency of light having the following wavelengths? 1.00 m 4.77 times 10_5 m 7894 A 1.903 times 10^3 m What is the wavelength of light having the given frequencies? 1.44 times 10^13s^-1 7.30 times 10^7 Hz 106.5 MHz 6.63 times 10^-3 s^-1 What is the energy of light having each characteristic? The Cu(H^2 O)_6^2+ complex has octahedral symmetry. Is a transition from a T_2g state to an E_g state allowed if the transition moment operator has a T_1u symmetry label?

Explanation / Answer

Frequency of light () and wavelength () related through speed of light (c) as,

= c/ or = c/

We know that Speed of light (c) = 3.0 x 108 m/s

14.4) Calculation of wavelength () for given frequencies ()

a) = 1.44 x 1013 s-1

= c/v

= (3.0 x 108) / (1.44 x 1013)

= 2.08 x 10-5 m ……….. (as speed of light in m/s used)

= 2.08 X 10 X 10-6 ………… (divide and multiplied by 10)

= 20.8 X 10-6 m

= 20.8 …………. (since, 10-6 m = 1)

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b) = 7.30 x 107 Hz = 7.30 x 107 s-1 …. (since, 1Hz = 1cycle per second i.e. s-1)

= (3.0 x 108) /(7.30 x 107)

= 4.11 m

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c)

= 106.5 MHz

= 106.5 x 106 Hz ………. (1MHz i.e. 1Mega Hertz = 106 Hertz)

= 1.065 x 108 Hz

= 1.065 x 108 s-1

Then,

= (3.0 x 108) / (1.065 x 108)

= 2.82 m

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d) = 6.63 x 10-3 s-1

= (3.0 x 108) /(6.63 x 10-3)

= 4.52 x 1010 m

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