A particle in a 453 m-long particle accelerator is moving at 0.875 c. How long d

Question

A particle in a 453 m-long particle accelerator is moving at 0.875 c. How long does the particle accelerator appear to the particle? 219 m 589 m 104 m 936 m 160 m The period of a pendulum clock is measured to be 3.00 s at rest. What is the period as measured by an observer moving at a speed of 0.950 c with respect to the clock? 0.937 s 9.61 s 13.4 s 0.671 s 3.00 s Assume that a typical city consumes electrical energy at a rate of 2.0 times 10^9 W. How many kilograms of matter would have to be converted entirely into energy in order to keep this city running for 147 days? 0.11 kg 0.15 kg 0.28 kg 0.32 kg 0.40 kg

Explanation / Answer

Wavelength of 1st line of Balmer series:

We know that 1/ = R [ 1/n1^2 - 1/n2^2] , = wavelength

Given that electron in a hydrogen atom undergoes the transition from the energy level n = 3 to the level n = 2

i.e. n1= 2 , n2= 3

Then,

1/ = R [1/n1^2 - 1/n2^2]

= R [ 1/2^2 - 1/3^2]

= R [ 1/4- 1/9]

= R (5/36)

1/ = R (5/36)

= (36/5) (1/R)

= (36/5) ( 91.17 nm) ( since R = 1.09678 x 10-2 nm-1 then 1/R = 91.17 nm)

= 656 nm

wavelength = 656 nm

Therefore,

wavelength of 1st line of Balmer series = 656 nm

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