Read the following text and answer the following questions on the basis of the same:
Electron Microscope
Electron microscopes use electrons to illuminate a sample. In Transmission Electron Microscopy (TEM), electrons pass through the sample and illuminate film or a digital camera. Resolution in microscopy is limited to about half of the wavelength of the illumination source used to image the sample. Using visible light the best resolution that can be achieved by microscopes is about `-200nm`. Louis de Broglie showed that every particle or matter propagates like a wave. The wavelength of propagating electrons at a given accelerating voltage can be determined by
`l= (h)/(sqrt(2m_(e )v))`. Thus the wavelength of electrons is calculated to be 3.88pm when the microscope is operated at 100keV, 2.74pm at 200keV and 2.24pm at 300keV. However, because the velocities of electrons in an electron microscope reach about 70% the speed of light with an accelerating voltage of 200keV, there are relativistic effects on these electrons. Due to this effect, the wavelength at 100keV, 200keV and 300keV in electron microscopes is 3.70pm, 2.51 pm and 1.96pm, respectively. Anyhow, the wavelength of electrons is much smaller than that of photons (2.5pm at 200keV). Thus if electron wave is used to illuminate the sample, the resolution of an electron microscope theoretically becomes unlimited. Practically, the resolution is limited to `~-0.1`nm due to the objective lens system in electron microscopes. Thus, electron microscopy can resolve subcellular structures that could not be visualized using standard fluorescences microscopy.
As the accelerating voltage increases, the wavelength of electron as wave

Options

A. decreases
B. increases
C. remains same
D. upto 100keV increases and then decreases.

Explanation

To solve the question regarding the effect of increasing accelerating voltage on the wavelength of electrons in an electron microscope, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The relationship between the wavelength (λ) of electrons and the accelerating voltage (V) is given by the formula:
\[ \lambda = \frac{h}{\sqrt{2m_e V}} \]
where \(h\) is Planck's constant, \(m_e\) is the mass of the electron, and \(V\) is the accelerating voltage.

2. **Analyzing the Formula**:
From the formula, we can see that the wavelength λ is inversely proportional to the square root of the accelerating voltage V. This means:
\[ \lambda \propto \frac{1}{\sqrt{V}} \]

3. **Effect of Increasing Voltage**:
If the accelerating voltage V increases, the square root of V also increases. Since λ is inversely proportional to \(\sqrt{V}\), an increase in V will lead to a decrease in λ.

4. **Conclusion**:
Therefore, as the accelerating voltage increases, the wavelength of the electrons decreases.

### Final Answer:
As the accelerating voltage increases, the wavelength of electrons as a wave **decreases**.

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