Step-by-Step Guidance for Physics Practice Exam #2

Q1. Why is it difficult to take a photo of an atom using an optical microscope?

Background

Topic: Wave Optics & Diffraction Limit

This question tests your understanding of the limitations of optical microscopes due to the wavelength of visible light and the phenomenon of diffraction.

Key Terms and Concepts:

• Diffraction: The bending of light waves around obstacles or through small openings, which limits the resolution of optical instruments.

• Wavelength of Light: The distance between successive peaks of a wave; visible light has wavelengths much larger than atomic dimensions.

• Resolution Limit: The smallest detail that can be distinguished by an optical system, typically on the order of the wavelength used.

Step-by-Step Guidance

1. Recall that the resolving power of an optical microscope is limited by the wavelength of visible light, which is typically between 400 nm and 700 nm.

2. Compare the size of an atom (about 0.1 nm) to the wavelength of visible light.

3. Understand that when the object is much smaller than the wavelength, diffraction causes the image to blur, making it impossible to resolve individual atoms.

4. Consider which statements (i) and (ii) accurately describe these limitations.

Try solving on your own before revealing the answer!

Q2. Which one of the following particles is the heaviest?

Background

Topic: Subatomic Particles and Mass Comparison

This question tests your knowledge of the relative masses of fundamental particles: protons, neutrons, electrons, and muons.

Key Terms:

• Proton: Positively charged particle in the nucleus.

• Neutron: Neutral particle in the nucleus, slightly heavier than a proton.

• Electron: Negatively charged particle, much lighter than protons and neutrons.

• Muon: A heavier cousin of the electron, about 207 times its mass.

Step-by-Step Guidance

1. Recall the approximate masses: proton (~1 u), neutron (~1 u, slightly heavier), electron (~1/1836 u), muon (~207 times electron mass).

2. Compare the masses of each particle listed in the options.

3. Identify which particle is the heaviest based on these comparisons.

Try solving on your own before revealing the answer!

Q3. What is an isotope?

Background

Topic: Atomic Structure

This question tests your understanding of isotopes and how atoms of the same element can differ.

Key Terms:

• Isotope: Atoms of the same element with the same number of protons but different numbers of neutrons.

• Proton Number (Atomic Number): Determines the element.

• Neutron Number: Varies among isotopes of the same element.

Step-by-Step Guidance

1. Recall that isotopes have the same number of protons but differ in the number of neutrons.

2. Review each option to see which one matches this definition.

3. Eliminate options that refer to differences in electrons or protons.

Try solving on your own before revealing the answer!

Q4. Which has the greater density; 100 grams of silver or 1000 grams of silver?

Background

Topic: Density and Intensive Properties

This question tests your understanding of density as an intensive property, which does not depend on the amount of substance.

Key Terms and Formula:

• Density ($\rho$): Mass per unit volume.

$\rho = \frac{m}{V}$

Step-by-Step Guidance

1. Recall that density is an intensive property, meaning it does not depend on the sample size.

2. Consider that both samples are pure silver, so their densities should be the same regardless of mass.

3. Review the options to see which reflects this concept.

Try solving on your own before revealing the answer!

Q5. The un-extended length of a spring is 1m. If a 200N weight is hung from it, it extends 10cm. If a 400N weight is hung from it, what is the new length of the spring?

Background

Topic: Hooke's Law and Elasticity

This question tests your ability to apply Hooke's Law to determine the extension of a spring under different loads.

Key Formula:

$F = k \Delta x$

• $F$ = force applied (in Newtons)

• $k$ = spring constant (N/m)

• $\Delta x$ = extension (in meters)

Step-by-Step Guidance

1. Use the first scenario to find the spring constant $k$: $k = \frac{F}{\Delta x}$, where $F = 200$ N and $\Delta x = 0.10$ m.

2. Calculate $k$ using these values (but do not compute the final value yet).

3. For the second scenario, use $F = 400$ N and the same $k$ to find the new extension $\Delta x_2$: $\Delta x_2 = \frac{F_2}{k}$

4. Add the new extension to the original length (1 m) to find the new length of the spring.

Try solving on your own before revealing the answer!