Assertion (A): $\beta$-glycosidic linkage is present in maltose. Reason (R): Maltose is composed of two glucose units in which C-1 of one glucose unit is linked to C-4 of another glucose unit. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false.

Assertion (A): β-glycosidic linkage is present in maltose. Reason (R): Maltose is composed of two glucose unit

NCERT Exemplar · Q67

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(i) Both A and R are true and R is the correct explanation of A.

(ii) Both A and R are true but R is not the correct explanation of A.

(iii) A is true but R is false.

(iv) Both A and R are false.

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Concept understanding — De Broglie Wavelength

De Broglie Wavelength: When Particles Start Acting Like Waves

Imagine you're holding a cricket ball. You know exactly where it is, and if you throw it, you can predict its path. That's a particle — localised, definite, following Newton's laws. Now think of light. You can't "hold" a beam of light; it spreads out, bends around corners, creates interference patterns. That's a wave — spread out, not localised.

For centuries, physics kept these two worlds separate. Particles were particles. Waves were waves. Never the twain shall meet.

Then came a young French physicist, Louis de Broglie, in 1924. He asked a question that seemed almost absurd: If light — which we thought was a wave — can behave like a particle (the photoelectric effect), then why can't a particle — say, an electron — behave like a wave?

That question turned physics upside down.

The Core Idea

De Broglie proposed that every moving particle has a wave associated with it. The wavelength of that wave depends on the particle's momentum. The faster or heavier the particle, the shorter the wavelength.

\lambda = \frac{h}{p} = \frac{h}{mv}

This is not a mathematical trick. It's a physical reality. An electron moving through a crystal actually behaves like a wave of this wavelength — it can diffract, interfere, and form patterns just like light does.

Why You Don't See It in Daily Life

Here's the crucial point: the de Broglie wavelength is incredibly tiny for everyday objects.

Take a cricket ball of mass 0.16 kg moving at 30 m/s. Its de Broglie wavelength is:

\lambda = \frac{6.626 \times 10^{-34}}{0.16 \times 30} \approx 1.38 \times 10^{-34} \ \text{m}

That's about a hundred trillion trillion times smaller than the nucleus of an atom. No experiment can detect such a wave — it's effectively zero for all practical purposes.

Now take an electron (mass $9.1 \times 10^{-31}$ kg) accelerated through 100 volts. Its speed is about $5.9 \times 10^6$ m/s. Its de Broglie wavelength:

\lambda = \frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 5.9 \times 10^6} \approx 1.23 \times 10^{-10} \ \text{m}

That's about 0.12 nanometres — comparable to the spacing between atoms in a crystal. This is measurable. And indeed, in 1927, Davisson and Germer fired electrons at a nickel crystal and observed diffraction — the unmistakable signature of a wave.

Note

The de Broglie wavelength is only observable when it is comparable to the size of objects the particle interacts with. For macroscopic objects, it's far too small to matter. For subatomic particles, it's the key to understanding their behaviour.

What This Means Physically

The wave is not a physical wave in space like a water wave. It's a probability wave — its amplitude at any point tells you the probability of finding the particle there. Where the wave amplitude is large, you're likely to find the particle; where it's zero, you won't.

This wave-particle duality is not a compromise. It's the actual nature of reality. An electron is neither a pure particle nor a pure wave — it's something that shows particle-like behaviour in some experiments (like hitting a screen at a point) and wave-like behaviour in others (like passing through two slits and interfering with itself). …

Why this formula?

De Broglie Wavelength: Why the Formula Holds

Let's build this from the ground up — understanding why matter has a wavelength, not just memorizing $\lambda = \frac{h}{p}$ .

The Core Insight: Nature's Symmetry

Before de Broglie, physics had two separate worlds:

Light — showed wave behaviour (diffraction, interference) but also particle behaviour (photoelectric effect)
Matter — showed particle behaviour (momentum, collisions) but no wave behaviour yet

De Broglie asked a daring question in his 1924 PhD thesis:

If light (a wave) can behave like a particle, why can't a particle (like an electron) behave like a wave?

Nature should be symmetric — what applies to one should apply to the other.

Step 1: Start with Light (What We Already Knew)

For a photon, Einstein had given us two key relations:

Energy: $E = hf$ (Planck's relation)
Momentum: $p = \frac{h}{\lambda}$ (from $E = pc$ for light, combined with $c = f\lambda$ )

So for light:

\lambda = \frac{h}{p}

This was experimentally verified for photons.

Step 2: De Broglie's Bold Hypothesis

De Broglie said: This relation is not special to light. It is universal.

For any particle with momentum $p$ :

\boxed{\lambda = \frac{h}{p}}

Where:

$\lambda$ = de Broglie wavelength
$h$ = Planck's constant ( $6.626 \times 10^{-34} \text{ J·s}$ )
$p$ = momentum of the particle

Step 3: Why Momentum and Not Velocity?

This is crucial. The formula uses momentum ( $p = mv$ ), not just velocity.

For a non-relativistic particle (slow compared to light):

\lambda = \frac{h}{mv}

For a relativistic particle (like an electron at high speed):

p = \gamma mv \quad \text{where} \quad \gamma = \frac{1}{\sqrt{1 - v^2/c^2}}

\lambda = \frac{h}{\gamma mv}

Why momentum? Because momentum is the more fundamental quantity — it's conserved, it's frame-independent in a deeper sense, and it connects directly to the wave's phase.

Step 4: The Deeper Reasoning — Wave-Particle Duality

De Broglie didn't just guess. He reasoned:

Every moving particle has an associated wave — called the "matter wave" or "pilot wave"
The frequency of this wave comes from energy: $f = \frac{E}{h}$
The wavelength comes from momentum: $\lambda = \frac{h}{p}$

These two relations are linked by the phase velocity of the wave:

v_{\text{phase}} = f\lambda = \frac{E}{h} \cdot \frac{h}{p} = \frac{E}{p}

For a free particle with kinetic energy $E = \frac{p^2}{2m}$ :

v_{\text{phase}} = \frac{p}{2m} = \frac{v}{2}

This is half the particle's speed — a strange but mathematically consistent result.

Step 5: Experimental Confirmation (Why We Believe It)

De Broglie's idea was confirmed when electrons showed wave behaviour: …

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Maltose has an $\alpha$ -(1→4) glycosidic linkage, not $\beta$ , so the Assertion is false. The Reason only states that C-1 of one glucose is linked to C-4 of the other — a true fact about connectivity that says nothing about $\alpha$ / $\beta$ . So Assertion is false and Reason is true, a combination none of the four listed options actually describes.

Evaluating the Assertion

Maltose is a disaccharide of two D-glucose units. The anomeric carbon (C-1) of the first glucose unit is in the $\alpha$ configuration, and it is this $\alpha$ -configured carbon that forms the glycosidic bond to C-4 of the second glucose unit. The bond is therefore an $\alpha$ -(1→4) glycosidic linkage — not $\beta$ . (Cellobiose, by contrast, has the analogous $\beta$ -(1→4) linkage; starch is built from $\alpha$ -linked glucose units like maltose, while cellulose is built from $\beta$ -linked ones.) So the Assertion is false.

Evaluating the Reason

The Reason states only that "C-1 of one glucose unit is linked to C-4 of another glucose unit" — this describes which carbons are bonded, and says nothing at all about whether that bond is $\alpha$ or $\beta$ . As a statement about maltose's connectivity, it is simply true.

Watch out

Do not conflate "which carbons are bonded" (the Reason's claim, true) with "what configuration the bond has" (the Assertion's claim, false). They are two different facts about the same linkage, and the Reason does not assert anything about $\alpha$ / $\beta$ that could make it false alongside the Assertion.

Matching to the options …

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Common Mistakes & How to Avoid Them

Mistake 1: Confusing $\alpha$ and $\beta$ glycosidic linkages

The error: Students think maltose has a $\beta$ -glycosidic linkage because they vaguely recall "maltose has a 1→4 linkage" and assume it's $\beta$ .

Why it's wrong: Maltose actually has an $\alpha$ -1,4-glycosidic linkage. The $\beta$ -1,4 linkage is found in cellobiose (a disaccharide from cellulose hydrolysis).

How to avoid: Memorise the key disaccharides with their linkage types:

Maltose → $\alpha$ -1,4
Cellobiose → $\beta$ -1,4
Lactose → $\beta$ -1,4
Sucrose → $\alpha$ -1,2 (between glucose and fructose)

Tip: Remember "Malt" (as in malted milk) is from starch breakdown — starch has $\alpha$ -linkages, so maltose inherits $\alpha$ .

Mistake 2: Assuming "C-1 to C-4" automatically means $\beta$

The error: Students match the Reason (R) statement — "C-1 of one glucose linked to C-4 of another" — and conclude it must be $\beta$ .

Why it's wrong: Both $\alpha$ and $\beta$ glycosidic bonds can be 1→4. The difference is the orientation of the bond:

$\alpha$ : the bond is below the plane of the glucose ring (axial)
$\beta$ : the bond is above the plane (equatorial)

How to avoid: Always check the anomeric carbon configuration, not just the carbon numbers. Draw the ring structures to see the difference.

Mistake 3: Thinking the Reason (R) is false

The error: Some students think R is wrong because they believe maltose links C-1 to C-2 or C-1 to C-6.

Why it's wrong: The Reason is correct — maltose does have a C-1 to C-4 linkage between two glucose units. The error is only in the Assertion (A), which calls it $\beta$ .

How to avoid: Read each statement independently. Verify facts separately:

Assertion (A): " $\beta$ -glycosidic linkage in maltose" → False (it's $\alpha$ )
Reason (R): "C-1 to C-4 linkage in maltose" → True

So the correct answer is (C) — A is false, R is true.

Mistake 4: Choosing option (A) or (B) without checking both statements …

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Q.Assertion (A): $\beta$ -glycosidic linkage is present in maltose.
Reason (R): Maltose is composed of two glucose units in which C-1 of one glucose unit is linked to C-4 of another glucose unit.

Concept understanding — De Broglie Wavelength

De Broglie Wavelength: When Particles Start Acting Like Waves

The Core Idea

Why You Don't See It in Daily Life

What This Means Physically

Why this formula?

De Broglie Wavelength: Why the Formula Holds

The Core Insight: Nature's Symmetry

Step 1: Start with Light (What We Already Knew)

Step 2: De Broglie's Bold Hypothesis

Step 3: Why Momentum and Not Velocity?

Step 4: The Deeper Reasoning — Wave-Particle Duality

Step 5: Experimental Confirmation (Why We Believe It)

Evaluating the Assertion

Evaluating the Reason

Matching to the options …

Method: Concept Verification with Structural Reasoning

Step 1: Verify the Assertion (A)

Step 2: Verify the Reason (R)

Step 3: Check the relationship

Final Answer

Common Mistakes & How to Avoid Them

Mistake 1: Confusing $\alpha$ and $\beta$ glycosidic linkages

Mistake 2: Assuming "C-1 to C-4" automatically means $\beta$

Mistake 3: Thinking the Reason (R) is false

Mistake 4: Choosing option (A) or (B) without checking both statements …

Q.Assertion (A): β\betaβ-glycosidic linkage is present in maltose. Reason (R): Maltose is composed of two glucose units in which C-1 of one glucose unit is linked to C-4 of another glucose unit.

Evaluating the Assertion

Evaluating the Reason

Matching to the options …

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Q.Assertion (A): $\beta$ -glycosidic linkage is present in maltose.
Reason (R): Maltose is composed of two glucose units in which C-1 of one glucose unit is linked to C-4 of another glucose unit.

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