HSC Science (Computer Science) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

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.

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.    

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

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. 

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. 

A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.

1. What is the rms value of current in the circuit?
2. What is the net power consumed over a full cycle?

The equation of a simple harmonic progressive wave travelling on a string is y = 8 sin (0.02x - 4t) cm. The speed of the wave is ______.

What is the mathematical formula for the third postulate of Bohr's atomic model?

Plane wavefront of Light of wavelength 6000 Å is incident on two slits on a screen perpendicular to the direction of light rays. If the total separation of 10 brights fringes on a screen 2m away is 2 cm, find the distance between the slits.

With the help of a neat diagram, explain the reflection of Light on a plane-reflecting surface.

Calculate the value of magnetic field at a distance of 3 cm from a very long, straight wire carrying a current of 6 A.

Explain de-Broglie wavelength.