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A radioactive isotope has a half-life of...

A radioactive isotope has a half-life of 27 days. Starting with 4g of the isotope, what will be mass remaining after 75 days

A

100 g

B

50 g

C

0.58 g

D

1.58 g

Text Solution

Verified by Experts

The correct Answer is:
C
`k= (0.693)/(t_(1//2))`
`t =(2.303)/k log (N_0)/(N)`
`t_(1//2) = 27 ` days
`k = (0.693)/(27) = 0.0257 "day"^(-1)`
`t= (2.303)/(0.0257) log (N_0)/N`
`N_0 = 4 g , N = ? , t = 75 ` days
`75= (0.0257) log N_0/N`
`N_0 = 4 g , N= ? , t= 75` days
`75 = (2.303)/(0.0257) log 4/N`
`N = 0.58 g `
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