The waves associated with electrons revolving in various Bohr orbits in an atom are -

Options

A. transverse
B. longitudinal
C. progressive
D. stationary

Answer

To solve the question about the nature of the waves associated with electrons revolving in various Bohr orbits in an atom, we can follow these steps:

### Step 1: Understand the Concept of Matter Waves
According to de Broglie's hypothesis, every moving particle, including electrons, has an associated wave. This wave is referred to as a matter wave. The wavelength (λ) of this wave can be calculated using the de Broglie equation:

\[ \lambda = \frac{h}{mv} \]

where \(h\) is Planck's constant, \(m\) is the mass of the particle, and \(v\) is its velocity.

**Hint:** Remember that de Broglie's hypothesis connects the wave nature of particles with their momentum.

### Step 2: Apply Bohr's Model of the Atom
In Bohr's model, electrons revolve around the nucleus in specific orbits, and the angular momentum of the electron in these orbits is quantized. The quantization condition is given by:

\[ L = mvr = n\frac{h}{2\pi} \]

where \(n\) is a positive integer (the principal quantum number).

**Hint:** The quantization of angular momentum is key to understanding the allowed orbits of electrons.

### Step 3: Relate Angular Momentum to Wavelength
From the angular momentum quantization condition, we can express the radius of the orbit in terms of wavelength. Rearranging the angular momentum equation gives:

\[ 2\pi r = n\lambda \]

This indicates that the circumference of the electron's orbit is an integer multiple of the wavelength of the associated wave.

**Hint:** Think about how the wave fits into the circular orbit of the electron.

### Step 4: Identify the Nature of the Waves
Since the wavelength fits into the circumference of the orbit, the waves associated with the electrons in these orbits are stationary waves. This means that the wave does not propagate away from the orbit but instead forms a standing wave pattern.

**Hint:** Stationary waves are characterized by nodes and antinodes and do not travel through space.

### Conclusion
The waves associated with electrons revolving in various Bohr orbits are stationary waves. This conclusion aligns with the de Broglie wavelength and the quantization of angular momentum in Bohr's model.

**Final Answer:** The waves associated with electrons revolving in various Bohr orbits in an atom are stationary waves.

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