Chemistry Q122 – AP-EAMCET 2026

Home Chemistry Dual Nature of MatterQuestion #379

The de Broglie wavelength associated with a pebble of mass

6.63 g

travelling with velocity

x {ms}^{- 1}

10^{- 24} nm

. What is the value of

x

(h = 6.63 \times 10^{- 34} Js)

Clue 1 of 3: Wave-Particle Duality

Remember that particles can exhibit wave-like properties, and their wavelength is inversely proportional to their momentum.

🧠 Full Solution Path

Step 1: Identify Given Values and Required Formula✦ Active

The problem asks for the velocity ( $x$ ) of a pebble given its mass ( $m$ ), de Broglie wavelength ( $λ$ ), and Planck's constant ( $h$ ). The relevant formula is the de Broglie wavelength equation:

λ = \frac{h}{m v}

💡 Teacher's Secret Hint

Ensure all units are consistent (SI units are preferred) before plugging values into the formula. Pay attention to powers of 10 in unit conversions.

Step 2: Convert Units to the SI System○ Expand

Convert the given mass from grams to kilograms and the de Broglie wavelength from nanometers to meters to ensure consistency with Planck's constant in Joules-seconds.

m = 6.63 g = 6.63 \times 10^{- 3} kg

λ = 10^{- 24} nm = 10^{- 24} \times 10^{- 9} m = 10^{- 33} m

h = 6.63 \times 10^{- 34} Js

💡 Teacher's Secret Hint

Recall that $1 g = 10^{- 3} kg$ and $1 nm = 10^{- 9} m$ . Common conversion errors can lead to incorrect powers of 10.

Step 3: Rearrange the Equation and Substitute Values○ Expand

Rearrange the de Broglie wavelength equation to solve for velocity ( $v$ ). Then, substitute the given and converted values into the equation.

v = \frac{h}{m λ}

v = \frac{6.63 \times 10^{- 34} Js}{(6.63 \times 10^{- 3} kg) \times (10^{- 33} m)}

v = \frac{6.63 \times 10^{- 34}}{6.63 \times 10^{- 3 - 33}}

v = \frac{6.63 \times 10^{- 34}}{6.63 \times 10^{- 36}}

v = 1 \times 10^{- 34 - (- 36)}

v = 1 \times 10^{2} {ms}^{- 1}

💡 Teacher's Secret Hint

Be careful with exponent arithmetic, especially when dividing powers of 10. Subtracting a negative exponent is equivalent to adding a positive exponent.

Step 4: State the Final Answer○ Expand

The calculated velocity is $1 \times 10^{2} {ms}^{- 1}$ . Therefore, the value of $x$ is $1.0 \times 10^{2}$ . This corresponds to option 2.

x = 1.0 \times 10^{2}

💡 Teacher's Secret Hint

Always double-check the units in the final answer. Velocity should be in ${ms}^{- 1}$ .

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Chemistry Question 122 – AP-EAMCET 2026

Clue 1 of 3: Wave-Particle Duality

🧠 Full Solution Path