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 effects cause the image to become blurry and indistinct.

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? (Note: A muon is 207 times heavier than an electron)

Background

Topic: Subatomic Particles and Their Masses

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

Key Terms and Concepts:

• Electron: A subatomic particle with a very small mass (~9.11 x 10-31 kg).

• Muon: Similar to an electron but heavier (207 times the mass of an electron).

• Proton: Mass ~1.67 x 10-27 kg.

• Neutron: Slightly heavier than a proton.

Step-by-Step Guidance

1. Recall the approximate masses of each particle listed.

2. Compare the mass of a muon to that of a proton and neutron.

3. Determine which particle is the heaviest among the options.

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 and Concepts:

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

• Atomic Number: Number of protons in the nucleus.

• Mass Number: Total number of protons and neutrons.

Step-by-Step Guidance

1. Recall the definition of an isotope.

2. Review the differences between protons, neutrons, and electrons in atomic structure.

3. Identify which option matches the definition of isotopes.

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 Concepts:

• Density (): , where is mass and is volume.

• Intensive Property: A property that does not depend on the amount of material present.

Step-by-Step Guidance

1. Recall the formula for density and what it means for a pure substance.

2. Consider whether changing the mass of silver changes its density.

3. Decide if 100 g and 1000 g samples of silver have different densities.

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 Terms and Formulas:

• Hooke's Law:

• = force applied (in Newtons)

• = spring constant (N/m)

• = extension (in meters)

Step-by-Step Guidance

1. Use the first scenario to find the spring constant using with N and m.

2. Set up the equation: .

3. Apply the value of to the second scenario where N to find the new extension .

4. Calculate the new length by adding the extension to the original length: .

Try solving on your own before revealing the answer!