de Broglie wavelength: Class 12 practice
Every moving particle has a wavelength λ = h/p = h/(mv). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Scientific notation
- Square roots
The idea behind de broglie wavelength
Every moving particle has a wavelength λ = h/p = h/(mv). For an electron accelerated through V volts, λ ≈ 1.227/√V nm.
Step-by-step method
- Find momentum p = mv (or from accelerating voltage).
- λ = h/p with h = 6.63 × 10⁻³⁴ J s.
- For electrons use λ = 1.227/√V nm.
Worked example 1 (Basic)
Find the de Broglie wavelength of a 50 g ball moving at 42 m/s.
- λ = h/mv
- = 3.157e-34 m
- Answer: 3.157e-34 m
Worked example 2 (Standard)
Find the de Broglie wavelength of an electron moving at 7e+6 m/s.
- λ = h/mv
- = 1.040e-10 m
- Answer: 1.040e-10 m
Worked example 3 (Challenge)
Find the de Broglie wavelength of an electron accelerated through 25 V.
- λ = 1.227/√25 nm
- = 0.245 nm
- Answer: 0.245 nm
Common mistakes and misconceptions
- Using mass in grams
- Forgetting the square root of V
Practice questions
- (Basic) Find the de Broglie wavelength of a 80 g ball moving at 30 m/s.
- (Basic) Find the de Broglie wavelength of a 90 g ball moving at 41 m/s.
- (Standard) Find the de Broglie wavelength of an electron moving at 5e+6 m/s.
- (Standard) Find the de Broglie wavelength of an electron moving at 3e+6 m/s.
- (Challenge) Find the de Broglie wavelength of an electron accelerated through 400 V.
- (Challenge) Find the de Broglie wavelength of an electron accelerated through 900 V.
Answer key with full working
- Q1: λ = h/mv → = 2.763e-34 m → Answer: 2.763e-34 m
- Q2: λ = h/mv → = 1.797e-34 m → Answer: 1.797e-34 m
- Q3: λ = h/mv → = 1.456e-10 m → Answer: 1.456e-10 m
- Q4: λ = h/mv → = 2.426e-10 m → Answer: 2.426e-10 m
- Q5: λ = 1.227/√400 nm → = 0.061 nm → Answer: 0.061 nm
- Q6: λ = 1.227/√900 nm → = 0.041 nm → Answer: 0.041 nm
Syllabus note
This skill is listed under "Dual Nature of Radiation and Matter" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is de broglie wavelength in?
"Dual Nature of Radiation and Matter", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.