Final answer:
Both statements provided by the student are true; electron microscopes can achieve better resolving power than optical microscopes because the electrons that they use have a much shorter de Broglie’s wavelength compared to the wavelength of visible light.
"the correct option is approximately option C"
Step-by-step explanation:
The student's question pertains to the comparison between the resolving power of an electron microscope and that of an optical microscope, and the underlying reason related to the de Broglie’s wavelength of electrons. Assertion A: An electron microscope can achieve better resolving power than an optical microscope is true. This is because the resolution of a microscope is determined, among other factors, by the wavelength of the probe used to observe the specimen. In this case, the electrons in an electron microscope have a much shorter wavelength than that of visible light used in optical microscopes.
Reason R: The de Broglie’s wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light is also true. Electrons used in electron microscopy are generated at high voltages, giving them very short wavelengths. These wavelengths are significantly shorter than the wavelengths of visible light, ranging from about 400 nm to 700 nm. As a result, the electron microscope can resolve much smaller details than the optical microscope.
Therefore, the correct answer to the student's question is C. Both A and R are true and R is the correct explanation of A. The de Broglie’s wavelength being shorter for electrons indeed explains why electron microscopes have greater resolving power than optical microscopes.