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13.Nuclei
easy
After $3$ hours, only $0.25 \,mg$ of a pure radioactive material is left. If initial mass was $2 \,mg$ then the half life of the substance is ...... $hr$
A
$1.5$
B
$1$
C
$0.5$
D
$2$
Solution
(b)
Initial mass $=2 \,mg$
Final mass $=0.25 \,mg$
$\therefore \frac{N}{N_0}=\left(\frac{1}{2}\right)^n$
$\frac{0.25}{2}=\left(\frac{1}{2}\right)^n$
$\frac{1}{8}=\left(\frac{1}{2}\right)^n$
$\therefore n=3$ and time is $3$ hours
Half life is therefore $1$ hour
Standard 12
Physics
Similar Questions
Match List $I$ (Wavelength range of electromagnetic spectrum) with List $II$ (Method of production of these waves) and select the correct option from the options given below the lists
| List $I$ | List $II$ |
| $(1)$ $700\, nm$ to $1\,mm$ | $(i)$ Vibration of atoms and molecules |
| $(2)$ $1\,nm$ to $400\, nm$ | $(ii)$ Inner shell electrons in atoms moving from one energy level to a lower level |
| $(3)$ $ < 10^{-3}\,nm$ | $(iii)$ Radioactive decay of the nucleus |
| $(4)$ $1\,mm$ to $0.1\,m$ | $(iv)$ Magnetron valve |
