Question

If the half-life of a substance is 3.8 days and its quantity is 10.38 gm. Then substance quantity remaining left after 19 days will be
A. 0.151 gm
B. 0.32 gm
C. 1.51 gm
D. 0.16 gm

Answer 1

Hint: As per the question, we need to find how much quantity of the substance will be left over after 19 days. We know that the half-life of a substance is 3.8 days, and the quantity of the substance is 10.38 gm. We will find the leftover substances by using the radioactive decay formula.

Formula Used
\[\dfrac{N}{{{N_0}}}\]= \[{(\dfrac{1}{2})^n}\]
Here, \[{N_0}\] is the amount of substance that will initially decay and \[N\] is the quantity that still remains.

Complete step by step solution:
Half-Life, formerly known as Half-Life Period, is one of the common terminologies used in Physics to define the radioactive decay of a certain sample or element within a specified period of time. This concept is also widely used to define different decay processes, particularly non-exponential and exponential decay.

To find out the number of half-life,
Number of half-lives \[n = \dfrac{{19}}{{3.8}}\] = 5
We know that,
\[\dfrac{N}{{{N_o}}}\]= \[{(\dfrac{1}{2})^n}\]
\[\Rightarrow \dfrac{N}{{10.38}} = {(\dfrac{1}{5})^5}\]
by substituting known values we get
\[N = 10.38 \times {(\dfrac{1}{2})^5}\]
$\therefore N= 0.32\,gm$
Therefore, after 19 days 0.32 gm of substance is left over.

Therefore the correct answer is option B.

Additional Information: The radioactive material can collapse on its own nucleus structure. Simultaneously, the nucleus radiates some small molecules or energy to the outside. The emitted particulate matter and radioactive energy can cause harm to human bodies.

In 1895, the German physicist Roentgen discovered X-rays, a type of radiation. Rontgen found that when the X-ray is projected directly onto the living body, an image of the bone is formed on the photosensitive plate. Among early experimentalists, Rutherford and his colleagues found three elements of radiation from radioactive substances. Such components were referred to as an α, β, and r-ray.

Later, those were recognised as electrons, nuclei of helium atoms, and high-energy photons. In radioactivity, Half-life is the interval of time needed for one-half of a radioactive sample's atomic nuclei to decompose. If the half-life moves again, half of the residual mass will remain. The mass is becoming smaller, but it always continues to be a bit.

Note: Students must remember the formula. So that they can easily find out the answer without any mistakes. Such type of problems can be solved if one should remember the formula.