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(D) The angular speed of the system is $\omega = 600 \,rev/s = 600 	imes 2\pi \,rad/s = 1200\pi \,rad/s$.For an atom to pass through the second slit,

Vedclass · Accepted Answer

$600, 200$

Vedclass · Answer

(D) The angular speed of the system is $\omega = 600 \,rev/s = 600 	imes 2\pi \,rad/s = 1200\pi \,rad/s$.For an atom to pass through the second slit,the second disc must rotate by an odd multiple of $\pi$ radians (i.e.,$\pi, 3\pi, 5\pi, \dots$) in the time $t$ it takes for the atom to travel the distance $L = 0.5 \,m$.The time taken is $t = L/v$.The angle rotated by the disc is $	heta = \omega t = \omega (L/v)$.For the slits to align,$	heta = (2n-1)\pi$ where $n = 1, 2, 3, \dots$.So,$\omega (L/v) = (2n-1)\pi$.$v = \frac{\omega L}{(2n-1)\pi} = \frac{1200\pi 	imes 0.5}{(2n-1)\pi} = \frac{600}{2n-1}$.For $n=1$,$v_1 = 600/1 = 600 \,m/s$.For $n=2$,$v_2 = 600/3 = 200 \,m/s$.Thus,the two largest speeds are $600 \,m/s$ and $200 \,m/s$.

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