Classically, anelectron can be in any orbit around the nucleus of an atom. Then whatdetermines the typical atomic size? Why is an atom not, say, thousandtimes bigger than its typical size? The question had greatly puzzledBohr before he arrived at his famous model of the atom that you havelearnt in the text. To simulate what he might well have done beforehis discovery, let us play as follows with the basic constants ofnature and see if we can get a quantity with the dimensions of lengththat is roughly equal to the known size of an atom (~ 10−10m).
(a) Construct a quantity with the dimensions of length fromthe fundamental constants e, me, andc. Determine its numerical value.
(b) You will find that the length obtained in (a) is manyorders of magnitude smaller than the atomic dimensions. Further, itinvolves c. But energies of atoms are mostly innon-relativistic domain where c is not expected to play anyrole. This is what may have suggested Bohr to discard c andlook for ‘something else’ to get the right atomic size.Now, the Planck’s constant h had already made itsappearance elsewhere. Bohr’s great insight lay in recognisingthat h, me, and e will yieldthe right atomic size. Construct a quantity with the dimension oflength from h, me, and e andconfirm that its numerical value has indeed the correct order ofmagnitude.
Classically, anelectron can be in any orbit around the nucleus of an atom. Then whatdetermines the typical atomic size? Why is an atom not, say, thousandtimes bigger than its typical size? The question had greatly puzzledBohr before he arrived at his famous model of the atom that you havelearnt in the text. To simulate what he might well have done beforehis discovery, let us play as follows with the basic constants ofnature and see if we can get a quantity with the dimensions of lengththat is roughly equal to the known size of an atom (~ 10−10m).
(a) Construct a quantity with the dimensions of length fromthe fundamental constants e, me, andc. Determine its numerical value.
(b) You will find that the length obtained in (a) is manyorders of magnitude smaller than the atomic dimensions. Further, itinvolves c. But energies of atoms are mostly innon-relativistic domain where c is not expected to play anyrole. This is what may have suggested Bohr to discard c andlook for ‘something else’ to get the right atomic size.Now, the Planck’s constant h had already made itsappearance elsewhere. Bohr’s great insight lay in recognisingthat h, me, and e will yieldthe right atomic size. Construct a quantity with the dimension oflength from h, me, and e andconfirm that its numerical value has indeed the correct order ofmagnitude.
(a) Charge on anelectron, e = 1.6 × 10−19 C
Massof an electron, me = 9.1 × 10−31kg
Speedof light, c = 3 ×108 m/s
Letus take a quantity involving the given quantities as 
Where,
∈0= Permittivity of free space
And,
Thenumerical value of the taken quantity will be:
Hence,the numerical value of the taken quantity is much smaller than thetypical size of an atom.
(b) Charge on an electron, e = 1.6 × 10−19C
Massof an electron, me = 9.1 × 10−31kg
Planck’sconstant, h = 6.63 ×10−34 Js
Letus take a quantity involving the given quantities as 
Where,
∈0= Permittivity of free space
And,
Thenumerical value of the taken quantity will be:
Hence,the value of the quantity taken is of the order of the atomic size.
(a) Charge on anelectron, e = 1.6 × 10−19 C
Massof an electron, me = 9.1 × 10−31kg
Speedof light, c = 3 ×108 m/s
Letus take a quantity involving the given quantities as
Where,
∈0= Permittivity of free space
And,
Thenumerical value of the taken quantity will be:
Hence,the numerical value of the taken quantity is much smaller than thetypical size of an atom.
(b) Charge on an electron, e = 1.6 × 10−19C
Massof an electron, me = 9.1 × 10−31kg
Planck’sconstant, h = 6.63 ×10−34 Js
Letus take a quantity involving the given quantities as
Where,
∈0= Permittivity of free space
And,
Thenumerical value of the taken quantity will be:
Hence,the value of the quantity taken is of the order of the atomic size.
