Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10–10m). (a) Construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.

(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.

Question

Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of nature and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10–10m). (a) Construct a quantity with the dimensions of length from the fundamental constants e, me, and c. Determine its numerical value.

(b) You will find that the length obtained in (a) is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for ‘something else’ to get the right atomic size. Now, the Planck’s constant h had already made its appearance elsewhere. Bohr’s great insight lay in recognising that h, me, and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.

Shivam Sharma · Accepted Answer

(a) Charge on an electron, e = 1.6 × 10⁻¹⁹C

Mass of an electron, m_e = 9.1 × 10⁻³¹ kg

Speed of light, c = 3 ×10⁸ m/s

Let us take a quantity involving the given quantities as

Where,

∈₀ = Permittivity of free space

And,

The numerical value of the taken quantity will be:

Hence, the numerical value of the taken quantity is much smaller than the typical size of an atom.

(b) Charge on an electron, e = 1.6 × 10⁻¹⁹C

Mass of an electron, m_e = 9.1 × 10⁻³¹ kg

Planck’s constant, h = 6.63 ×10⁻³⁴ Js

Let us take a quantity involving the given quantities as

Where,

∈₀ = Permittivity of free space

And,

The numerical value of the taken quantity will be:

Hence, the value of the quantity taken is of the order of the atomic size.

I am a Student I am a Tutor
Name*	Please enter your full name. Please enter institute name.
Email*	Please enter your email address.
Phone*	Please enter a valid phone number.
Location*	Please enter a pincode or area name.
City*	Please enter city name.
Category*	Please enter category.
Gender*	Male Female Please select your gender.
Email ID/ Mobile No.*	Please enter either mobile no. or email.
Enter Password*	Please enter OTP Please enter Password Sorry, this phone number is not verified, Please login with your email Id.

Looking for Class 12 Tuition Classes?

Take Class 12 Tuition with the Best Tutors