Problem 16 - Master Resource Book in JEE Main Physics

Question

The specific charge for positive rays is much less than that for cathode rays. This is because (a) masses of positive rays are much larger (b) charge on positive ray is less (c) positive rays are positively charged (d) experiment method is wrong

Step-by-Step Solution

Answer

The specific charge for positive rays is much less because masses of positive rays are much larger (Option a).

Step 1: Identify the Concepts

The specific charge is defined as the ratio of charge to mass, often described as \( \frac{Q}{m} \). Cathode rays are streams of electrons with a high specific charge due to their small mass and a consistent charge of one electron. Positive rays, on the other hand, are composed of positive ions, which typically have a much larger mass compared to a single electron, though their charges can be similar.

Step 2: Analyze the Options

Let's consider each provided option: (a) suggests that the mass of positive rays is much larger; (b) implies the charge on positive rays is less; (c) states that positive rays are positively charged; (d) claims the experiment method is wrong.

Step 3: Assess Each Option

Option (a): A large mass causes a decrease in specific charge because \( \frac{Q}{m} \) becomes smaller as the mass \( m \) is increased, assuming \( Q \) remains constant. This supports the specific charge being less.Option (b): If the charge \( Q \) were less, this would also reduce the specific charge. However, positive rays generally have charges similar to electrons but greater mass, countering this assertion.Option (c): Although positive rays are positively charged, this fact does not inherently explain a smaller specific charge as compared to electrons.Option (d): Incorrect experimental methods could result in incorrect findings but wouldn't universally explain all experimental outcomes regarding specific charges.

Step 4: Determine the Correct Explanation

Considering the above analysis, the reason why the specific charge of positive rays is much less than that for cathode rays relates to the significantly larger mass of positive ions compared to electrons. Thus, Option (a) is the most plausible explanation.

Key Concepts

Cathode Rays

Cathode rays are streams of electrons that were first discovered in vacuum tubes. These rays are invisible but can be detected by their ability to make certain materials glow or fluoresce.
They travel in straight lines and are deflected by electric and magnetic fields, indicating they include charged particles. Cathode rays consistently have a negative charge because they consist primarily of electrons.

One key characteristic of cathode rays is their high specific charge. Specific charge refers to the ratio of charge to mass (\( \frac{Q}{m} \)).

• Electrons have a small mass, making the denominator in the calculation of specific charge small, thereby giving a higher overall value.
• The charge of one electron is roughly \(-1.6 \times 10^{-19}\) coulombs.

Because of this small mass and consistent charge, cathode rays have a much higher specific charge than positive rays.

Positive Rays

Positive rays, often referred to as canal rays, are beams of positive ions produced when particles move in the opposite direction to the cathode rays in a discharge tube.
Under the influence of an electric field, they travel towards the cathode. Julius Plücker first observed them when he noticed a glow on the side opposite the cathode in his experiments with gas discharge tubes.

These rays consist of positive ions, which means they have lost one or more electrons, resulting in a net positive charge. They have a lower specific charge than cathode rays due to their mass.

• Typically, the atoms or molecules that form positive rays are much heavier than electrons.
• Their positive charge comes from losing electrons but the magnitude of charge isn’t significantly less than that of an electron. The mass, however, is much larger.

This results in a smaller specific charge \( \frac{Q}{m} \), since the mass \( m \) in the denominator grows significantly.

Mass of Ions

The mass of ions is crucial when discussing the behavior of positive rays and their specific charge. Positive ions in rays are formed when atoms or molecules lose electrons, usually due to an external energy source like electricity.
This makes these ions much more massive than a single electron, which greatly affects their specific charge.

The mass of these ions is typically on the order of atomic nuclei, significantly larger than that of an electron.

• Common positive ions in such rays come from hydrogen, helium, or other light gases, but even these carry much more mass compared to electrons.
• This increased mass in the denominator of the specific charge ratio (\( \frac{Q}{m} \)) results in a much smaller specific charge value compared to cathode rays.

Thus, when calculating the specific charge of positive rays, the increased mass of ions is the primary reason for the lower figure compared to cathode rays.