Dual Nature Of Matter

Step 1: Concept
The shortcut formula for an electron's de-Broglie wavelength is .
Step 2: Analysis
Given .
.
Step 3: Conclusion
.
Final Answer: (B)

Step 1: Concept
The relationship between wavelength and kinetic energy ( ) is .
Step 2: Analysis
This implies . If becomes , the new wavelength .
Step 3: Conclusion
The wavelength changes by a factor of .
Final Answer: (A)

Step 1: Concept
De-Broglie wavelength .
Step 2: Analysis
Given: , , . .
Step 3: Conclusion
.
Final Answer: (B)

Step 1: Oxidation of X
Compound X is oxidized by to form a product that reacts with phenyl hydrazine. This indicates the product is a carbonyl compound (aldehyde or ketone).
Step 2: Negative Tollen's Test
The product fails the silver mirror test, meaning it is a ketone, not an aldehyde.
Step 3: Precursor Identification
Ketones are produced by the oxidation of secondary alcohols. Among the options, (isopropyl alcohol) is the secondary alcohol.
Final Answer: (c)

Step 1: Formaldehyde Formation
Dry distillation of calcium formate alone yields methanal (formaldehyde).
Step 2: Acetone Formation
Dry distillation of calcium acetate alone yields propanone (acetone).
Step 3: Acetaldehyde Formation
Distilling the mixture together yields ethanal (acetaldehyde). Propanal cannot be formed from these specific starting materials.
Final Answer: (b)

Step 1: Intensity Relation
Intensity ( ) follows the inverse square law: .
Step 2: Amplitude Relation
Intensity is also proportional to the square of the amplitude ( ): . Thus, , which means .
Step 3: Calculation
.
Final Answer: (b)

Concept: De-Broglie wavelength:

Step 1: Proton case

Step 2: Alpha particle

Step 3: Ratio