Question

At what constant rate $P$ , ${}^{56}Mn$ nuclei are being produced in the cyclotron during the bombardment?
A. \[2 \times {10^{11}}nuclei{s^{ - 1}}\]
B. \[13.86 \times {10^{10}}nuclei{s^{ - 1}}\]
C. \[9.6 \times {10^{10}}nuclei{s^{ - 1}}\]
D. \[6.93 \times {10^{10}}nuclei{s^{ - 1}}\]

Answer 1

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

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

Thus, \[13.86 \times {10^{10}}\] stable \[Mn\] 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.