Advertisements
Advertisements
प्रश्न
Show that the density of nucleus over a wide range of nuclei is constant-independent of mass number A.
उत्तर
To find the density of nucleus of an atom, we have an atom with mass number lets say A. (Here, we are neglecting mass of the orbital electrons)
Mass of the nucleus of the atom of the mass number A.
= A a.m.u
= A × 1.660565 × 10−27 kg
Let radius of nucleus is R.
Then,volume of nucleus, `=4/3 piR^3`
`= 4/3 pi (R_0A^(1/3))^3`
`=4/3 piR_0^3A`
Now, we know R0 = 1.1 × 10−15 m
∴Volume of nucleus` 4/3 pi (1.1 xx 10^-15)^3 xx Am^3`
Density of the nucleus
`δ = (\text { Mass of nucleus})/(\text { Volume of nucleus})`
`= (A xx 1.6605 xx 10^-27)/(4/3pi (1.1 xx 10^-15)^3 xx A)`
`= 2.97 xx 10^17 kgm^-3`
Thus, we can see the density of nuclei is independent of the mass number and is constant for all nuclei.
APPEARS IN
संबंधित प्रश्न
In the study of Geiger-Marsdon experiment on scattering of α particles by a thin foil of gold, draw the trajectory of α-particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study.
From the relation R = R0 A1/3, where R0 is constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A
The three stable isotopes of neon: `""_10^20"Ne"`, `""_10^21"Ne"` and `""_10^22"Ne"` have respective abundances of 90.51%, 0.27% and 9.22%. The atomic masses of the three isotopes are 19.99 u, 20.99 u and 21.99 u, respectively. Obtain the average atomic mass of neon.
The nucleus `""_10^23"Ne"` decays by `beta^(-)`emission. Write down the β decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:
`"m"(""_10^23 "Ne")` = 22.994466 u
`"m"(""_11^23 "Na")` = 22.989770 u.
Two nuclei have mass numbers in the ratio 1: 2. What is the ratio of their nuclear densities?
Find the Q-value and the kinetic energy of the emitted α-particle in the α-decay of `""_86^220"Rn"`.
Given `"m"(""_88^226"Ra")` = 226.02540 u, `"m"(""_86^222 "Rn")` = 222.01750 u,
`"m"(""_86^220 "Rn")`= 220.01137 u, `"m"(""_84^216 "Po")`= 216.00189 u.
Nuclear species or nuclides are shown by the notation ________ where X is the chemical symbol of the species.
\[\ce{^197_79Au}\] contains ______.
A nucleus of mass number A has a radius R such that ______.
A nucleus yYx emits one α and two β particles. The resulting nucleus is ______.
Before the neutrino hypothesis, the beta decay process was throught to be the transition, `n -> p + vece`. If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.
