Can anyone please help with the solution to this problem? Separation of ionized

Question

Can anyone please help with the solution to this problem?

Separation of ionized potassium isotopes

You have a natural mixture of potassium isotopes to separate, mostly the lighter 39K, mass 38.9637 u, but a few percent of the mixture is 41K, the heavy potassium isotope, mass 40.9618 u. They are singly ionized: 39K+ and 41K+. Shoot them through our example calutron from lecture, but with voltage dipped to 2000 volts for safety. In the calutron, each isotope makes a 90 degree turn in the magnetic field. They do land close to each other but are separated. Make a careful, simple sketch of the curved tracks. Calculate speeds of each isotope after acceleration (to the nearest 1 m/s), radius of curvature for each isotope's track (to the nearest 0.001 m) and the separation distance D between their landing points (to the nearest 0.001 m). For clarity, use L as subscript for the light isotope 39K's properties, and use subscript H for the heavy 41K isotope's properties, e.g., rH. 1.00000 u = 1.66054x10-27 kg.

Explanation / Answer

mv2/2= eV, V = 2000 volt , e = 1.6* 10-19C , mL = 38.9637 g

MH = 40.9618 g .

On putting the value of mass, charge of the electron, voltage we can find out the velocity of both isotopes

vL= 4.053 *10-7 m/s ,   H = 3.95* 10-7 m/s,

r = mv/eH after knowing the value of H we can find out the radius of curvature, where m is mass of the atom, v is speed, e is charge and H is magnetic field strength.

Seperatio distance between them is =2rH- 2rL.

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