De Broglie wavelength of proton = \(λ\) and that of an a particle \(2λ\). The ratio of velocity of proton to that of \(\alpha\) particle is
- \(8\)
- \(\frac{1}{8}\)
- \(4\)
- \(\frac{1}{4}\)
The Correct Option is B
Solution and Explanation
The correct option is (B): \(\frac{1}{8}\)
Top Questions on de broglie hypothesis
If \( \lambda \) and \( K \) are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be:
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- A proton accelerated through a potential difference of V volts has a de-Broglie wavelength \(\lambda\) associated with it. In order to get the same wavelength associated with an \(\alpha\)-particle, the required accelerating potential is
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- The de-Broglie wavelength associated with a ball of mass 150 g traveling at 30.0 m/s would be
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Questions Asked in JEE Main exam
If \( S \) and \( S' \) are the foci of the ellipse \[ \frac{x^2}{18} + \frac{y^2}{9} = 1 \] and \( P \) is a point on the ellipse, then \[ \min (SP \cdot S'P) + \max (SP \cdot S'P) \] is equal to:
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- Conic sections
- The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be
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- System of Particles & Rotational Motion
- Let ABC be a triangle formed by the lines \( 7x - 6y + 3 = 0 \), \( x + 2y - 31 = 0 \), and \( 9x - 2y - 19 = 0 \). Let the point \( (h, k) \) be the image of the centroid of \( \triangle ABC \) in the line \( 3x + 6y - 53 = 0 \). Then \( h^2 + k^2 + hk \) is equal to:
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- Coordinate Geometry
Given below are two statements I and II.
Statement I: Dumas method is used for estimation of "Nitrogen" in an organic compound.
Statement II: Dumas method involves the formation of ammonium sulfate by heating the organic compound with concentrated H\(_2\)SO\(_4\). In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Nitrogen
Considering Bohr’s atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of He+ ion in its first excited state.
(B) the energy of H atom in ground state is same as that for Li++ ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of He+ ion for its ground state.
(D) the energy of He+ ion in its first excited state is same as that for Li++ ion in its ground state.- JEE Main - 2025
- Atomic Models
Concepts Used:
De Morgans Theorem
De-Morgan's First Theorem
As per De-Morgan's first theorem, the complement outcomes of the AND operation are equivalent to the OR operation of the complement of that variable. Thus, it is equivalent to the NAND function and is a negative-OR function manifest that (A.B)' = A'+B' and we can show this using the given table.
De-Morgan's Second Theorem
As per De-Morgan's second theorem, the complement outcomes of the OR operation are equivalent o the AND operation of the complement of that variable. Thus, it is the equal of the NOR function and is a negative-AND function that manifests that (A+B)' = A'.B' and we can represent this using the given truth table.
