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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Question

Chapter 29, Problem 68GP

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 67GP

Chapter 29, Problem 69GP

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