SCERT Maharashtra solutions for Physics [English] 12 Standard HSC chapter 15 - Structure of Atoms and Nuclei [Latest edition]

When an electron jumps from a higher energy orbit to a lower energy orbit, the difference in the energies in the two orbits is radiated as quantum (photon) of ______  

The radii of Bohr orbit are directly proportional to ______ 

According to Bohr's second postulate, the angular momentum of the electron is the integral multiple of `h/(2pi)`. The S.I unit of Plank constant h is the same as ______ 

The ionization energy of Hydrogen atom in its ground state is ______.

For the hydrogen atom, the minimum excitation energy ( of n =2) is ______

The dimensions of Rydberg’s constant are ______ 

In Hydrogen, the electron jumps from the fourth orbit to the second orbit. The wavenumber of the radiations emitted by an electron is ______  

The speed of electron having de Broglie wavelength of 10 ^-10 m is ______ 
(m_e = 9.1 × 10^-31 kg, h = 6.63 × 10^-34 J-s) 

The decay constant λ of a certain radioactive material is 0.2166 per day. The average life τ of the radioactive material is ______ 

The ratio of areas of the circular orbit of an electron in the ground state to that of the first excited state of an electron in a hydrogen atom is ______  

What is the angular momentum of an electron in the first excited state for a hydrogen atom? 

If a_O is the Bohr radius and n is the principal quantum number then, state the relation for the radius of n^th orbit of the electron in terms of Bohr radius and principal quantum number. 

In which region of the electromagnetic spectrum for Hydrogen, does the Lyman series lies? 

How much energy must be supplied to a hydrogen atom, to free (remove) the electron in the ground state? 

State the value of minimum excitation energy for the Hydrogen atom. 

What is the energy of an electron in a hydrogen atom for n = ∞?  

The radius of the smallest orbit of the electron( a_O) in a hydrogen atom is 0.053 nm. What is the radius of the 4^th orbit of the electron in a hydrogen atom?  

The half-life of a certain radioactive species is 6.93 × 10⁵ seconds. What is the decay constant?  

The linear momentum of the particle is 6.63 kg m/s. Calculate the de Broglie wavelength.

Starting with 𝑟 = `(ε_0h^2n^2)/(pimZe^2),` Show that the speed of an electron in n^th orbit varies inversely to principal quantum number. 

State Bohr's second postulate for the atomic model. Express it in its mathematical form.  

State any two limitations of Bohr’s model for the hydrogen atoms. 

Using de Broglie’s hypothesis, obtain the mathematical form of Bohr’s second postulate.

Show that half life period of radioactive material varies inversely to decay constant λ.

Define the Excitation energy of an electron in an atom.

Define: Ionization energy.

Calculate the longest wavelength in the Paschen series.

(Given R_H =1.097 ×10⁷ m^-1)  

The angular momentum of an electron in the 3^rd Bohr orbit of a Hydrogen atom is 3.165 × 10^-34 kg m²/s. Calculate Plank’s constant h.    

The half-life of a certain radioactive nucleus is 3.2 days. Calculate (i) decay constant (ii) average life of radioactive nucleus.

Draw a neat labelled diagram showing energy levels and transition between them for the hydrogen atoms. 

Derive an expression for the radius of the n^th Bohr orbit for the hydrogen atom.

Using the expression for the energy of an electron in the n^th orbit, Show that `1/lambda = "R"_"H"(1/"n"^2 - 1/"m"^2),` Where symbols have their usual meaning. 

Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.

Obtain an expression for the half-lifetime of radioactive material. Hence state the relation between an average life and half lifetime of radioactive material.  

Calculate the wavelength for the first three lines in the Paschen series. 
(Given R_H =1.097 ×10⁷ m^-1)  

Calculate the shortest wavelength in the Paschen series if the longest wavelength in the Balmar series is 6563 A^o. 

A radioactive substance decays to (1/10)^th of its original value in 56 days. Calculate its decay constant. 

State the postulates of Bohr’s atomic model. Hence show the energy of electrons varies inversely to the square of the principal quantum number. 

Obtain an expression for wavenumber, when an electron jumps from a higher energy orbit to a lower energy orbit. Hence show that the shortest wavelength for the Balmar series is 4/R_H.  

Obtain an expression for the decay law of radioactivity. Hence show that the activity A(t) =λN_O e^-λt.  

Using the expression for the radius of orbit for the Hydrogen atom, show that the linear speed varies inversely to the principal quantum number n the angular speed varies inversely to the cube of principal quantum number n.