enEnglishhiहिन्दी
JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
An \(\alpha\) particle and a carbon \(12\) atom has same kinetic energy \(K\). The ratio of their de-Broglie wavelength \(\left(\lambda_{a}: \lambda_{C 12}\right)\) is
- A \(1: \sqrt{3}\)
- B \(\sqrt{3}: 1\)
- C \(3: 1\)
- D \(2: \sqrt{3}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{3}: 1\)
Step-by-step Solution
Detailed explanation
\(k=\frac{P^{2}}{2 m} \Rightarrow P \alpha \sqrt{m}\) Now \(\lambda=\frac{h}{p}\) So, \(\lambda \alpha \frac{1}{p} \Rightarrow \lambda \alpha \frac{1}{\sqrt{m}}\) \(\frac{\lambda_{\alpha}}{\lambda_{C 12}}=\frac{\sqrt{3}}{1}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A physical quantity \(P\) is given as \(P=\frac{a^2 b^3}{c \sqrt{d}}\) The percentage error in the measurement of \(a, b, c\) and \(d\) are \(1 \%, 2 \%, 3 \%\) and \(4 \%\) respectively. The percentage error in the measurement of quantity \(P\) will be \(.......\%\)JEE Mains 2023 Easy
- The reading of the ammeter (A) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is _________ A.
JEE Mains 2026 Easy - The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of \(3 rd\) orbit will be \(.........R\)JEE Mains 2023 Easy
- A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of \(25 \pi \mathrm{Nm}\) for 40 s, the speed increases to 2100 rpm. The diameter of the disk is ________ m.JEE Mains 2025 Medium
- The temperature of a body in air falls from \(40^{\circ} \mathrm{C}\) to \(24^{\circ} \mathrm{C}\) in 4 minutes. The temperature of the air is \(16^{\circ} \mathrm{C}\). The temperature of the body in the next 4 minutes will be:JEE Mains 2025 Medium
- Different combination of \(3\) resistors of equal resistance \(R\) are shown in the figures.
The increasing order for power dissipation is:
JEE Mains 2023 Medium
More PYQs from JEE Mains
- In the circuit diagram shown in figure given below, the current flowing through resistance \(3\, \Omega\) is \(\frac{ x }{3}\,A\). The value of \(x\) is \(...........\)
JEE Mains 2023 Hard - The number of positive integers \(k\) such that the constant term in the binomial expansion of \(\left(2 x^{3}+\frac{3}{x^{k}}\right)^{12}, x \neq 0\) is \(2^{8} \cdot \ell\), where \(\ell\) is an odd integer, is......JEE Mains 2022 Medium
- Each of the angles \(\beta\) and \(\gamma\) that a given line makes with the positive y - and z -axes, respectively, is half of the angle that this line makes with the positive x -axes. Then the sum of all possible values of the angle \(\beta\) isJEE Mains 2025 Medium
- Let \(a_1,a_2,a_3,....,a_{10}\) be in \(G.P.\) with \(a_i > 0\) for \(i = 1, 2,....,10\) and \(S\) be the set of pairs \((r,k), r, k \in N\) (the set of natural numbers) for which \(\left| {\begin{array}{*{20}{c}}
{{{\log }_e}\,a_1^ra_2^k}&{{{\log }_e}\,a_2^ra_3^k}&{{{\log }_e}\,a_3^ra_4^k} \\
{{{\log }_e}\,a_4^ra_5^k}&{{{\log }_e}\,a_5^ra_6^k}&{{{\log }_e}\,a_6^ra_7^k} \\
{{{\log }_e}\,a_7^ra_8^k}&{{{\log }_e}\,a_8^ra_9^k}&{{{\log }_e}\,a_9^ra_{10}^k}
\end{array}} \right| = 0\) Then the number of elements in \(S\), isJEE Mains 2019 Hard - Given below are two statements: Statement \(I:\) For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases. Statement \(II:\) Escape velocity is independent of the radius of the planet. In the light of above statements, choose the most appropriate answer from the options given below on :JEE Mains 2023 Medium
- Two transparent media having refractive indices \(1.0\) and \(1.5\) are separated by a spherical refracting surface of radius of curvature \(30\,cm\). The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of \(15\,cm\) from the pole of the surface. The distance of image from the pole of the surface is .......\(cm\)JEE Mains 2023 Medium