Question

A radioactive substance Technetium-99 is also used by physicians to examine blood flow to

specific organs and assess organ function or bone growth. It has a very short half-life of about 6

hours. The fraction of this material that would remain after 30 hours will be-

a) 1/32

b) 1/5

c) 1/2

d) 4/5​

Answer 1

Given - Half life of Technetium-99 - 6 hours.

Given time - 30 hours.

Find - Fraction of Technetium-99 that will remain after 30 hours.

Solution - To find the fraction, the formula used will be - {(1/2)^n}*original mass. In the formula, n refers to number of half lives.

Further, n is calculated as - 30/6 - 5

Thus, number of half lives - 5

Therefore, keeping the values in first formula - 1/2⁵ - 1/32*original mass.

Thus, option a) 1/32 is the correct answer.

Answer 2

Given : A radioactive substance Technetium-99 has a very short half-life of about 6 hours.  

To Find : The fraction of this material that would remain after 30 hours

1/32

b) 1/5

c) 1/2

d) 4/5

Solution:

Ley say initial Amount = A

after 6 hrs  = A/2

After 6 + 6 = 12 hrs = (A/2)/2 = A/4

After 12 + 6 = 18 hrs = (A/4)/2 = A/8

After 18 + 6 = 24 hrs = (A/8)/2 = A/16

After 24 + 6 = 30 hrs = (A/16)/2  = A/32  

= (1/32)A

Hence 1/32  fraction of this material that would remain after 30 hours

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