JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
A proton and an \(\alpha\)-particle are accelerated from rest by \(2\,V\) and \(4\,V\) potentials, respectively. The ratio of their de-Broglie wavelength is:
- A \(4:1\)
- B \(2:1\)
- C \(8:1\)
- D \(16:1\)
Answer & Solution
Correct Answer
(A) \(4:1\)
Step-by-step Solution
Detailed explanation
\(\lambda=\frac{ h }{ mv }=\frac{ h }{\sqrt{2 mK }}=\frac{ h }{\sqrt{2 mq \Delta V }}\) \(\frac{\lambda_\alpha}{\lambda_p}=\sqrt{\frac{m_p V_p q_p}{ m _\alpha V_\alpha q_\alpha}}\)…
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
- In an \(LCR\) series circuit, an inductor \(30 \,{mH}\) and a resistor \(1 \, \Omega\) are connected to an \(AC\) source of angular frequency \(300 \, {rad} / {s}\). The value of capacitance for which, the current leads the voltage by \(45^{\circ}\) is \(\frac{1}{x} \times 10^{-3} \, {F}\). Then the value of \(x\) is ..... .JEE Mains 2021 Hard
- The acceleration due to gravity at height \(h\) above the earth if \(h \ll R\) (radius of earth) is given byJEE Mains 2023 Medium
- Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz, then the original frequency of tuning fork A is ___________ Hz.JEE Mains 2026 Easy
- An inductor of \(10\) mH, capacitor of \(0.1\ \mu\)F and a resistor of \(100\ \Omega\) are connected in series across an \(a.c\) power supply \(220\) V, \(70\) Hz. The power factor of the given circuit is \(0.5\). The difference in the inductive reactance and capacitance reactance is \(\sqrt{3}\alpha\ \Omega\). The value of \(\alpha\) is _____.JEE Mains 2026 Medium
- A source and a detector move away from each other in absence of wind with a speed of \(20\, {m} / {s}\) with respect to the ground. If the detector detects a frequency of \(1800\, {Hz}\) of the sound coming from the source, then the original frequency of source considering speed of sound in air \(340\, {m} / {s}\) will be \({Hz}\)JEE Mains 2021 Easy
- The electric current in a circular coil of four turns produces a magnetic induction \(32\,T\) at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be \(..........\,T\)JEE Mains 2023 Easy
More PYQs from JEE Mains
- If \(n\) be odd or even, then the sum of \(n\) terms of the series \(1 - 2 + \) \(3 - \)\(4 + 5 - 6 + ......\) will beJEE Mains 2022 Easy
- A line with direction ratios \(1, -1, 2\) intersects the lines \(\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z+1}{3}\) and \(\dfrac{x+1}{-1} = \dfrac{y-2}{1} = \dfrac{z}{4}\) at the points \(P\) and \(Q\), respectively. If the length of the line segment \(PQ\) is \(\alpha\), then \(225\alpha^2\) is equal to:JEE Mains 2026 Hard
- Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude. Reason \(R \): At equator, the direction of acceleration due to the gravity is towards the center of earth. In the light of above statements, choose the correct answer from the options given belowJEE Mains 2022 Medium
- Let the numbers \(2, b, c\) be in an \(A.P\) and \(A = \left[ {\begin{array}{*{20}{c}}
1&1&1 \\
2&b&c \\
4&{{b^2}}&{{c^2}}
\end{array}} \right]\). If \(det(A) \in [2,16]\) then \(c\) lies in the intervalJEE Mains 2019 Hard - A particle moves such that its position vector \(\overrightarrow{\mathrm{r}}(\mathrm{t})=\cos \omega \mathrm{t} \hat{\mathrm{i}}+\sin \omega \mathrm{t} \hat{\mathrm{j}}\) where \(\omega\) is a constant and \(t\) is time. Then which of the following statements is true for the velocity \(\overrightarrow{\mathrm{v}}(\mathrm{t})\) and acceleration \(\overrightarrow{\mathrm{a}}(\mathrm{t})\) of the particleJEE Mains 2020 Medium
- Let \(A =\{0,1,2, \ldots 9)\). Let R be a relation on A defined by \(( x , y ) \in R\) if and only if \(| x - y |\) is a multiple of 3 .
Given below are two statements:
Statement I: \(n ( R )=36\)
Statement II: \(R\) is an equivalence relation.
In the light of the above statements, choose the correct answer from the options given belowJEE Mains 2026 Hard