Can anyone please help with the solution to this problem? Separation of ionized
ID: 706542 • Letter: C
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.