Let the mass of the electron be m and mass of the nucleus be M. Since there is no external force acting on the system, the centre of mass of hydrogen atom remains at rest. Hence, both nucleus and electron move about the centre of mass as shown in figure.

Let V be the velocity of the nuclear motion and υ be the velocity of electron motion. Since the total linear momentum of the system is zero,
−mሀ + Mሀ = 0 or
Mሀ = mሀ = p
\(\vec { { p }_{ e } } +\vec { { p }_{ n } } =\vec { 0 } \) or
\(|\vec { { p }_{ e } } |=|\vec { { p }_{ n } } |=p\)
Hence, the kinetic energy of the system is
KE = \(\frac { { { p }^{ 2 } }_{ n } }{ 2M } +\frac { { { p }^{ 2 } }_{ e } }{ 2m } =\frac { { p }^{ 2 } }{ 2 } \left( \frac { 1 }{ M } +\frac { 1 }{ m } \right) \)
Let \(\frac { 1 }{ M } +\frac { 1 }{ m } =\frac { 1 }{ { \mu }_{ m } } \). Here the reduced mass is
\({ \mu }_{ m }=\frac { mM }{ M+m } \)
Therefore, the kinetic energy of the system now is
\(KE=\frac { { p }^{ 2 } }{ { 2\mu }_{ m } } \)
Since the potential energy of the system is same, the total energy of the hydrogen can be expressed by replacing mass by reduced mass, which is
\({ E }_{ n }=-\frac { { \mu }_{ m }{ e }_{ 4 } }{ 8{ \epsilon ^{ 2 } }_{ 0 }{ h }^{ 2 } } \frac { 1 }{ { n }^{ 2 } } \)
Since the nucleus is very heavy compared to the electron, the reduced mass is closer to the mass of the electron.

(i) Angular momentum is given by
l = nħ = \(\frac { nh }{ 2\pi } \)
= \(\frac { 5\times 6.6\times { 10 }^{ -34 } }{ 2\times 3.14 } \) = 5.25 x 10^-34 kgm²s^-1
(ii) Velocity is given by
Velocity \(\nu =\frac { l }{ mr } \)

v = 4.4 x 10⁵ms⁻¹

(i) An atom has a nucleus surrounded by electrons
(ii) Nucleus is made up of protons and neutrons.
(iii) Till 1960s, it was thought that protons, neutrons and electrons are fundamental building blocks of matter.
(iv) In 1964, physicists Murray Gellman and George Zweig theoretically proposed that protons and neutrons are not fundamental particles in fact they are made up of quarks.
(v) These quarks are now considered elementary particles of nature.
(vi) Electrons are fundamental or elementary particles because they are not made up of anything.
(vii) In the year 1968, the quarks were discovered experimentally by Stanford Linear Accelerator Center (SLAC), USA.
(viii) There are six quarks namely, up, down, charm, strange, top and bottom and their antiparticles.
(ix) All these quarks have fractional charges. For example, charge of up quark is + \(\frac23\) e and that of down quark is \(\frac13\) e.
(x) According to quark model, proton is made up of two up quarks and one down quark and neutron is made up of one up quark and two down quarks.

From equation (9.19), the radius of the nuclecus, R = R₀ \(A^\frac13\). Then the volume of the nucleus
\(V=\frac { 4 }{ 3 } \pi { R }^{ 3 }=\frac { 4 }{ 3 } { \pi { R }_{ 0 } }^{ 3 }A\)
By ignoring the mass difference between the proton and neutron, the total mass of the nucleus having mass number A is equal to A.m where m is mass of the proton and is equal to 1.6726 x 10^-27 kg.
Nuclear density.

The element chlorine is a mixture of 75.77% of  \(_{ 17 }^{ 35 }{ Cl }\) and 24.23% of  \(_{ 17 }^{ 37 }{ Cl }\). So the average atomic mass will be
\(\frac { 75.77 }{ 100 } \times 34.96885u+\frac { 24.23 }{ 100 } \times 36.96593u\)
= 35.453 u
In fact, the chemist uses the average atomic mass or simply called chemical atomic weight (35.453 u for chlorine) of an element. So it must be remembered that the atomic mass which is mentioned in the periodic table is basically averaged atomic mass.