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 |
$(1)-(iv), (2)-(iii), (3)-(ii), ( 4)-(i)$
$(1)-(iii), (2)-(iv), (3)-(i), (4)-(ii)$
$(1)-(ii), (2)-(ii i), (3)-(iv), (4)-(i)$
$(1)-(i), (2)-(ii), (3)-(iii), (4)-(iv)$
The decay constant of a radio active substance is $0.173\, (years)^{-1}.$ Therefore :
Half-lives of two radioactive elements $A$ and $B$ are $20$ minutes and $40$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80$ minutes, the ratio of decayed number of $A$ and $B$ nuclei will be
Draw a graph showing the variation of decay rate with number of active nuclei.
At any instant, two elements $X _1$ and $X _2$ have same number of radioactive atoms. If the decay constant of $X _1$ and $X _2$ are $10 \lambda$ and $\lambda$ respectively. then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively will be
The half-life period of radium is $1600 $ years. Its average life time will be.......years