﻿ The half-life of a radioactive substance is  against . Calculate the decay rate for  atoms of the substance. : Kaysons Education

# The Half-life Of A Radioactive Substance Is  against . Calculate The Decay Rate For  atoms Of The Substance.

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## Question

### Solution

Correct option is

According to Rutherford and Soddy law, the rate of radioactive decay at any time t is given by

where  is decay constant and N is the number of atoms left at time t. If Tbe the half-life, then

Substituting this value of  atoms in eq. (i), we get

.

#### SIMILAR QUESTIONS

Q1

The half-life of radon is 3.8 days. Calculate how mach radon will be left out of 1024 milligram after 38 days?

Q2

1 milligram radium has . Its half-life is 1620 years. How many radium atoms will disintegrate from 1 milligram of pure radium in 3240 years?

Q3

A sample of radioactive substance has 106 radioactive nuclei. Its half-life time is 20 seconds. How many nuclei will remain after 10 seconds?

Q4

A sample contains 10–2 kg each of the two substances A and B with half-lives 4 seconds and 8 seconds respectively. Their atomic weights are in the ratio of 1 : 2. Find the amounts of A and B after an interval of 16 seconds.

Q5

The half-life of radius is 1600 years. After how many years 25% of a radium block remains undecayed?

Q6

The half-life of polonium is 140 days. In what time will 15 g of polonium be disintegrated out of its initial mass of 16 g?

Q7

The activity of a radioactive element reduces to th of its original value in 30 years. Find the half-life and the decay constant of the element.

Q8

The half-life of thorium-X is 3.64 days. After how many days will 0.1 of the mass of a sample of the substance remain undecayed?

Q9

How much of 5.00 gram of polonium will decay in one year? The half-life of polonium is 138 days.

Q10

The half-life of  against . Calculate the activity of 1 g sample of . Avogadro’s number is .