a. Explanation Given data: Wavelength is 254 nm. Diameter is 15 mm. Length is 25 cm. Power is 4.5 W. Pressure is 1 Pa. Temperature is 40 ° C . Formula used: Ideal gas law is given by, p V = N k B T (1) Here, p is the pressure. V is the volume. N is the number of atoms. k B is the rydberg constant, which has a standard value of 1.38 × 10 − 23 J K . T is the temperature. Work function equation E = h c λ (2) Here, h is the planks constant, which has a standard value as 6.63 × 10 − 34 J ⋅ s , c is the speed of light , which has a standard value as 3 × 10 8 m s , λ is the wavelength. Volume is given by, V = π r 2 l (3) Here, r is the radius. l is the length. Explanation: Modify equation (1) with respect to equation (3) p ( π r 2 l ) = N k B T N = p ( π r 2 l ) k B T (4) radius= diameter 2 Substitute 15 mm for diameter, radius= 15 mm 2 = 7.5 mm Substitute 7.5 mm for r , 25 cm for l , 1 Pa for p , 1.38 × 10 − 23 J K for k B , and 40 ° C for T in equation (4), N = 1 Pa ( π ( 7.5 mm ) 2 ( 25 cm ) ) 1.38 × 10 − 23 J K × 40 ° C = 1 Pa ( π ( 7.5 × 10 − 3 m ) 2 ( 0.25 m ) ) 1.38 × 10 − 23 J K × ( 40 +273 K ) = 1 Pa ( π ( 5.625 × 10 − 5 m 2 ) ( 0.25 m ) ) 1.38 × 10 − 23 J K × ( 313 K ) = 1 b. To determine The fraction of time mercury atom spend in the excited state.

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Chapter 29, Problem 66GP

To determine

The number of ultraviolet photons each mercury atom emit per second.

To determine

The fraction of time mercury atom spend in the excited state.

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Chapter 29, Problem 65GP

Chapter 29, Problem 67GP

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