Question

Initial mass of a radioactive substance is 3.2 mg. It has a half-life of 4 h. Find the mass of the substance left undecayed after 8 h.

Solution
Verified by Toppr

Given data :-
Initial Mass $$= M_0 = 3.2 mg$$

$$t_{1/2} = 4 m$$

To calculate , mass of the substance left undecayed after $$8h \, [M_z = 8]$$
we know,

$$M_{(z)} = M_0 e^{-\lambda t}$$

$$\dfrac{M_0}{2} = M_0 e^{-\lambda (4)}$$

$$\Rightarrow \lambda = \dfrac{1}{4} \ln (2)$$

$$M_{(8)} = M_0 . e^{-\lambda . 8}$$

$$\Rightarrow M_{(8)} = M_0 . e^{-\dfrac{1}{4} . \ln (2) . 8}$$

$$M_{(8)} = M_0 e^{-2 \ln (2)}$$

$$M = \left(\dfrac{M_0}{4} \right)$$

$$= \dfrac{3.2 mg}{4}$$

$$M_{(8)} = 0.8 mg $$

Was this answer helpful?
0
Similar Questions
Q1

what % of a given mass of a radioactive substance will be left undecayed after four half lives

View Solution
Q2

A radioactive substance decays to 1/16th of its initial mass in 40 days. The half life of the substance, in days, is?

View Solution
Q3

If 78th of the initial mass of a radioactive substance decays in 15 days, then what is the half-life period of the radioactive substance?

View Solution
Q4

The half life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would be:

View Solution
Q5

In a sample of a radioactive substance, what friction of the initial nuclei will remain undecayed after a time t=T/2, where T= half-life of radioactive substance?

View Solution
Solve
Guides