Question

Please show your work. (Note: 1.08 is incorrect, but the 10^-1 is correct.)

Be sure to answer all parts. If 5.01 x 10-9 mol of 176w emits 1.07 x 1015 β+ in 1.00 h, what is the decay constant? Enter your answer in scientific notation. 1.08 x 10 h1 -1 h-l

Answer 1

Solution:

1 mol of W-176 contains 6.023 x 10^23 nuclei

Hence, 5.01 x 10^-9 mol contains = 6.023 x 10^23 x 5.01 x 10^-9 = 3.018 x 10^15 nuclei

According to disintegration equation,

N = No e ^-kt

Where, k = disintegration constant, No = 3.018 x 10^15

, N =1.07 x 10^15 and t =1 hour

Above equation is also written as,

ln N = ln No -kt

-kt = ln N - ln No

-kt  = ln ( N / No)

-kt = ln(1.07 x 10^15 / 3.018 x 10^15 )

-kt =log 2.303 x 0.3545 =log 0.8164

-k x 1 hour = - 0.08809

k = 0.8809 x10^-1 hour^-1