Which of the following statement is not correct about the characteristics of cathode rays? (i) They start from

NCERT Exemplar · Q4

Q. Which of the following statement is not correct about the characteristics of cathode rays?

(i) They start from the cathode and move towards the anode.

(ii) They travel in straight line in the absence of an external electrical or magnetic field.

(iii) Characteristics of cathode rays do not depend upon the material of electrodes in cathode ray tube.

(iv) Characteristics of cathode rays depend upon the nature of gas present in the cathode ray tube.

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Concept understanding — Scale Analogy

Scale Analogy

Why we need an analogy at all

Rutherford's gold-foil experiment revealed something almost impossible to picture: the atom's entire positive charge and nearly all of its mass sit inside a nucleus that is fantastically smaller than the atom around it. The numbers are so extreme that our everyday intuition breaks down — so physicists reach for a scale analogy: blow the atom up to a size we can imagine, and see where the nucleus ends up.

The intuition: the atom is mostly empty space

Most alpha particles fired at the gold foil passed straight through, barely deflected. Only about 1 in 8000 bounced back sharply. The only way to explain this is that the atom is overwhelmingly empty, with a tiny, dense, positively charged core that the occasional alpha particle scores a near-direct hit on.

So how tiny is "tiny"? Compare the two sizes:

Radius of a typical atom: about $1 \times 10^{-10}\ \text{m}$ ( $1\ \text{angstrom}$ )
Radius of a typical nucleus: about $1 \times 10^{-15}\ \text{m}$ ( $1\ \text{femtometre}$ )

The ratio is

\frac{r_{\text{atom}}}{r_{\text{nucleus}}} \approx \frac{10^{-10}\ \text{m}}{10^{-15}\ \text{m}} = 10^{5}

The atom is about one hundred thousand times wider than its nucleus.

Making the number imaginable

A factor of $10^5$ is just a symbol on paper. The scale analogy converts it into something the mind can hold:

If the nucleus were the size of a pea (about $1\ \text{cm}$ across), then the atom would be a sphere roughly $10^5$ times bigger — around $1\ \text{km}$ across. The pea would sit alone at the centre of a stadium-sized region of empty space, with the electrons whirling somewhere out near the edge.
Equivalently, if the atom were scaled up to the size of a large sports ground, the nucleus would be no bigger than a grain of sand at the centre-spot.

Either picture drives home the same point: an atom is almost entirely empty space, which is exactly why nearly every alpha particle sailed through the foil undeflected.

Density: the flip side of the analogy

The scale analogy also warns us about density. Nearly the whole mass of the atom is squeezed into that pin-point nucleus. Because volume grows as the cube of the radius, shrinking the mass-holder by $10^5$ in radius packs it into a volume $10^{15}$ times smaller. That is why nuclear matter has an almost unimaginable density — on the order of $10^{17}\ \text{kg/m}^3$ — while the atom as a whole is light and airy. …

Why this formula?

Scale Analogy

One of the hardest facts to picture in atomic physics is just how empty an atom is. Rutherford's scattering experiment showed that almost all the mass sits in a tiny central nucleus, with the electrons far outside. A scale analogy makes the numbers vivid.

The nucleus is about $10^{-15}\ \text{m}$ across while the whole atom is about $10^{-10}\ \text{m}$ — the atom is roughly 100,000 times wider than its nucleus, so it is almost entirely empty space.

The Sizes Involved

Atomic radius: $r_{\text{atom}} \approx 10^{-10}\ \text{m}$ (1 angstrom).
Nuclear radius: $r_{\text{nucleus}} \approx 10^{-15}\ \text{m}$ (1 femtometre).

The ratio of diameters is:

\frac{r_{\text{atom}}}{r_{\text{nucleus}}} \approx \frac{10^{-10}}{10^{-15}} = 10^{5}

Bringing It to Human Scale

Imagine blowing the nucleus up to the size of a cricket ball (radius $\approx 3.5\ \text{cm}$ ). To keep the same ratio, the electrons would orbit at:

0.035\ \text{m}\times 10^{5} = 3500\ \text{m} \approx 3.5\ \text{km}

So a nucleus the size of a ball at the centre of a stadium would have its electrons drifting kilometres away — and the space in between is vacuum. …

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Cathode rays are identical for all gases and electrode materials — only the gas’s identity affects the positive rays (canal rays), not the cathode rays themselves. The incorrect statement is (D).

The key to this question is understanding what cathode rays actually are: streams of electrons. Electrons are fundamental particles, identical whether they come from a copper electrode, a platinum one, or any other material. They are also the same whether the tube contains hydrogen, helium, or neon. The gas in the tube does affect how easily the discharge happens (the voltage needed) and what colour the glow is, but the cathode rays themselves — their charge, mass, and behaviour — are independent of the gas.

Let’s examine each statement carefully.

Statement (A): “They start from the cathode and move towards the anode.”

This is correct. Cathode rays are emitted from the negative electrode (cathode) when a high voltage is applied across a low-pressure gas. They are attracted to the positive electrode (anode) because they carry a negative charge. This is the fundamental definition of cathode rays.
Statement (B): “They travel in straight line in the absence of an external electrical or magnetic field.”

This is also correct. Like any charged particle beam with no external forces, cathode rays move in straight lines. This is why they cast sharp shadows of objects placed in their path — a classic experiment by Crookes.
Statement (C): “Characteristics of cathode rays do not depend upon the material of electrodes in cathode ray tube.”

Correct again. J.J. Thomson and others showed that the charge-to-mass ratio ( $e/m$ ) of cathode rays is the same regardless of the electrode material. Whether you use iron, aluminium, or platinum, the particles are identical electrons. The material only affects how easily electrons are emitted (work function), not the nature of the rays.
Statement (D): “Characteristics of cathode rays depend upon the nature of gas present in the cathode ray tube.” …

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Q.Which of the following statement is not correct about the characteristics of cathode rays?

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