Question
A muonic hydrogen atom is a bound state of a negativelycharged muon of mass 207m_{e} and a proton and the muon orbits around the proton. Obtain the radius of its first Bohr orbit.




2.58 X 10^{17}
medium
Solution
The radius of first (n = 1) Bohr orbit of hydrogen atom (Z = 1) is given by
.
The radius of the first orbit of muonic atom will be
.
SIMILAR QUESTIONS
A beam of particles of velocity is scattered by a gold (Z = 79) foil. Find out the distance closest approach of the particle to the gold nucleus. The value of charge/mass for particle is .
What is the upper limit of the radius of the gold nuclues (Z = 79), if an particle of energy 12.5 MeV is deflected back by the nucleus through 180^{o}.
In a headon collision between an particle and gold (Z = 79) nucleus, the closest distance of approach is 41.3 fermi. Calculate the energy of the particle. (1 fermi = 10^{–15 }m)
Write down the expression for the radii of orbits of hydrogen atom. Calculate the radius of the smallest orbit.
In Bohr’s model of hydrogen atom, the radius of the first electron orbit is 0.53 Å. What will be the radius of the third orbit? What of the first orbit of singlyionised helium atom?
Which energy state of the triply ionized beryllium (Be^{+++}) has the same orbital radius as that of the ground state of hydrogen? Compare the energies of the two states.
Calculate the speed of an electron revolving in the first orbit around the nucleus of a hydrogen atom in order that in order that it may not be pulled into the nucleus by electrostatic attraction.
Determine the speed of electron in the n = 3 orbit of He^{+}. Is the nonrelativistic approximation valid? Datas as above.
The total energy (potential + kinetic) of an electron in the ground state of Bohr model of hydrogen atom is –13.6 eV. Obtain the values of the potential energy U and kinetic energy K in eV. Include –ve or +ve sign as required.
The energy of an electron in an excited hydrogen atom is –3.4 eV. Calculate the angular momentum of the electron according to Bohr’s theory. Planck’s constant .