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To solve this problem, note that when a charged particle with mass m and charge q is fired perpendicular to a magnetic field of strength B, it undergoes uniform circular motion. The period (time to complete one full circle) is given by:

Here's how to calculate it step by step:
Convert the given quantities to SI units:
Charge:
Mass:
Magnetic field:

Write down the period formula:

Substitute the values:

Notice that , which cancels with the given magnetic field value, simplifying the expression:

Simplify the fraction:

Thus, the time required for the particle to return to its original location is: