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प्रश्न
The radius of \[\ce{^27_13X}\] nucleus is R. The radius of \[\ce{^125_53Y}\] nucleus will be ______.
पर्याय
`5/3R`
`(13/53)^{1"/"3}R`
`(5/3R)^{1"/"3}`
`(13/53R)^{1"/"3}`
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उत्तर
The radius of \[\ce{^27_13X}\] nucleus is R. The radius of \[\ce{^125_53Y}\] nucleus will be `underlinebb(5/3R)`.
Explanation:
As given in the question,
\[\ce{^27_13X -> X}\] is aluminium as the atomic number of aluminium is 13 and the mass number is 27.
\[\ce{^125_53Y -> Y}\] is the tellurium as the atomic number of tellurium is 53 and the mass number is 125.
Radius of the nucleus, R = `R_0(A)^{1"/"3}`
So, `R ∝ A^{1"/"3}`
So, `R_{Al}/R_{Te} = sqrt(27/125)`
`R_{Te} = (125/27)^{1"/"3} xx R`
`R_{Te} = 5/3R`
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संबंधित प्रश्न
The ratio of the nuclear densities of two nuclei having mass numbers 64 and 125 is ______.
The stable nucleus that has a radius half that of Fe56 is:
The Q value of a nuclear reaction A + b → C + d is defined by Q = [mA + mb − mC − md]c² where the masses refer to the respective nuclei. Calculate the Q-value of the reaction and state whether this reaction is exothermic or endothermic.
\[_1^1\mathrm{H}+_1^3\mathrm{H}\rightarrow_1^2\mathrm{H}+_1^2\mathrm{H}\]
Atomic masses are given to be
\[\mathrm{m(}_{1}^{1}\mathrm{H)}=1.007825\mathrm{u}\]
\[\mathrm{m(}_{1}^{2}\mathrm{H)}=2.014102\mathrm{u}\]
\[\mathrm{m(}_{1}^{3}\mathrm{H})=3.016049\mathrm{u}\]
Assertion (A): All nuclei are not of the same size.
Reason (R): The size of the nucleus depends on atomic mass.
How is the nuclear radius defined?
The value of the radius constant \[R_0\] used in the nuclear radius formula is approximately:
Which experiments provide more accurate measurements of nuclear size and help determine the distribution of charge inside the nucleus?
Since the nucleus is approximately spherical with \[R = R_0 A^{1/3}\], its volume \[V = \frac{4}{3}\pi R^3\] is proportional to:
The approximate density of nuclear matter is:
The density of matter in a neutron star is:
