Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Using Huygens’s construction of secondary wavelets draw a diagram showing the passage of a plane wavefront from a denser to a rarer medium. Using it verifies Snell’s law.

(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?

(ii) Find the relation between three wavelengths λ₁, λ₂ and λ₃ from the energy-level diagram shown below.

State Bohr’s postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom. Use Rydberg formula to determine the wavelength of H_α line. [Given: Rydberg constant R = 1.03 × 10⁷ m⁻¹]

Write symbolically the nuclear β⁺ decay process of `""_6^11C` Is the decayed product X an isotope or isobar of (`""_6^11C`)? Given the mass values m (`""_6^11C`) = 11.011434 u and m (X) = 11.009305 u. Estimate the Q-value in this process.

Is the nucleus formed in the decay of the nucleus `""_11^22Na`, an isotope or isobar?

Using Bohr's postulates of the atomic model, derive the expression for radius of n^th electron orbit. Hence obtain the expression for Bohr's radius.

What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state?

The energy associated with the first orbit in the hydrogen atom is - 2.18 × 10^-18 J atom^-1. What is the energy associated with the fifth orbit?

Calculate the radius of Bohr’s fifth orbit for hydrogen atom

What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10^–11 ergs.

Explain, giving reasons, which of the following sets of quantum numbers are not possible.

1. n = 0, l = 0, ml = 0, ms = + ½
2. n = 1, l = 0, ml = 0, ms = – ½
3. n = 1, l = 1, ml = 0, ms = + ½
4. n = 2, l = 1, ml = 0, ms = – ½
5. n = 3, l = 3, ml = –3, ms = + ½
6. n = 3, l = 1, ml = 0, ms = + ½

How many electrons in an atom may have the following quantum numbers?

n = 4, `m_s =  -1/2`

How many electrons in an atom may have the following quantum numbers?

n = 3, l = 0

Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

Calculate the energy required for the process 

\[\ce{He^+_{(g)} -> He^{2+}_{(g)} + e^-}\]

The ionization energy for the H atom in the ground state is 2.18 ×10^–18 J atom^–1

Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 10¹⁵, calculate the energy of the source.

The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.

If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 10⁷ ms^–1, calculate the energy with which it is bound to the nucleus.

If the velocity of the electron in Bohr’s first orbit is 2.19 × 10⁶ ms^-1, calculate the de Broglie wavelength associated with it.

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is

1. a convex lens of focal length 20 cm, and
2. a concave lens of focal length 16 cm?