Quantum Mechanics | MCQs

Explanation

If the speed of a moving particle increases, the wavelength associated with it will decrease. 

This is due to the relationship between wavelength and momentum in the de Broglie equation, where wavelength is inversely proportional to velocity. 

Explanation

The reverse process of the photoelectric effect is the production of X-rays when electrons are decelerated.

In the photoelectric effect, light (photons) interacts with a material, causing electrons to be emitted.

Explanation

• Energy
• Momentum
• Charge

Explanation

The energy of a photon is calculated using the formula E = hf, where:

• h = Planck’s constant
• f = frequency of the photon

This shows that photon energy is directly proportional to its frequency.

Explanation

- Given: n = 4, l = 3

- When l = 3, it's an f-subshell

- The number of orientations = number of magnetic quantum number (mₗ) values = 2l + 1

- So, 2(3) + 1 = 7

Explanation

 The lifetime of an electron in a metastable state is significantly longer than in an ordinary excited state, typically by 10³ to 10⁵ times. 

Ordinary excited states have lifetimes on the order of 10⁻⁸ seconds. 

Metastable states have lifetimes that can range from microseconds to milliseconds and even longer, being orders of magnitude longer than typical excited states.

Therefore, options like 10³ or 10⁵ are appropriate estimations for how much longer a metastable state lifetime is compared to an ordinary excited state. 

Explanation

 The maximum number of electrons in an atom is given by the formula:  

Total electrons = 2n²  

For n = 4:  

2(1² + 2² + 3² + 4²) = 2(1 + 4 + 9 + 16) = 2(30) = 60  

But this is a misunderstanding. Each shell holds:

- n=1: 2  

- n=2: 8  

- n=3: 18  

- n=4: 32  

So total = 2 + 8 + 18 + 32 = 60, but this is not per atom.  

If n = 4 is the maximum principal quantum number, then the 4th shell is being filled.  

The maximum number of electrons that can exist in the 4th shell is:  

2n² = 2(4)² = 32

Explanation

When atomic orbitals (like s and p) mix to form hybrid orbitals (e.g., sp³, sp², sp),

The resulting orbitals have the same energy — they are degenerate.

This uniform energy level allows for equal bond strength and geometry, such as in methane (CH₄) with four sp³ orbitals.

Explanation

If the maximum value of the principal quantum number (n) for an atom is 4, the total number of electrons in that atom is 32.

This is because the maximum number of electrons in a shell is given by 2n², and for n=4, this calculation results in 2 * 4² = 32. 

Explanation

The total energy of a hydrogen atom in its ground state is negative. 

The energy of a hydrogen atom in its ground state is typically represented as -13.6 eV.

A negative energy value indicates that the electron is bound to the nucleus and requires energy to be overcome to escape.

The ground state is the lowest energy level an electron can occupy in a hydrogen atom.