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Question: At what constant rate \(P\) , \({}^{56}Mn\) nuclei are being produced in the cyclotron during the bo...

At what constant rate PP , 56Mn{}^{56}Mn nuclei are being produced in the cyclotron during the bombardment?
A. 2×1011nucleis−12 \times {10^{11}}nuclei{s^{ - 1}}
B. 13.86×1010nucleis−113.86 \times {10^{10}}nuclei{s^{ - 1}}
C. 9.6×1010nucleis−19.6 \times {10^{10}}nuclei{s^{ - 1}}
D. 6.93×1010nucleis−16.93 \times {10^{10}}nuclei{s^{ - 1}}

Explanation

Solution

In order to this question, to know the constant rate when 56Mn{}^{56}Mn nuclei are being produced in the cyclotron during the bombardment, we will write the equation to explain the constant rate when 56Mn{}^{56}Mn nuclei are being produced in the cyclotron during the bombardment.

Complete step by step answer:
56Mn+d→56Mn(stable)+P{}^{56}Mn + d \to {}^{56}Mn(stable) + P
One radioactive MnMn nucleus disintegrates to convert to one stable MnMn nucleus. After a long time, the activity of 56Mn{}^{56}Mn becomes equal to 13.86×1010nucleis−113.86 \times {10^{10}}nuclei{s^{ - 1}} . That means, 13.86×1010nucleis−113.86 \times {10^{10}}nuclei{s^{ - 1}} radioactive MnMn nuclei get disintegrated in one second.

Thus, 13.86×101013.86 \times {10^{10}} stable MnMn nuclei are produced in one second. A cyclotron accelerates charged particles outwards in a spiral route from the centre. A static magnetic field keeps the particles on a spiral path, while a rapidly fluctuating (radio frequency) electric field accelerates them.

Hence, the correct option is B.

Additional-Information: A cyclotron is a particle accelerator invented by Ernest O. Lawrence at the University of California, Berkeley, between 1929 and 1930 and patented in 1932. A cyclotron accelerates charged particles outwards along a spiral path from the centre of a flat cylindrical vacuum chamber. A static magnetic field keeps the particles on a spiral path, while a rapidly fluctuating (radio frequency) electric field accelerates them. Lawrence received the Nobel Prize in Physics in 1939 for this discovery.

Note: Fluorine-18 can be produced using both cyclotrons and linear accelerators.Fluorine-18 that has been generated with a cyclotron is used in most PET factories. The cyclotron is used to attack target nuclei with deuterons or protons that have been accelerated.