# Problem: The de Broglie relation λ=h/p can be rewritten in terms of the wave number k as p=kℏ. Recall that wave number is defined by k=2π/λ.(a) Using the fact that λ=v/f, find the wave numbers k1 and k2 corresponding to frequencies f1 and f2. Express your answer as two expressions separated by a comma. Use f1, f2, v, and π.(b) Find an expression for the uncertainty Δk=k1−k2 in the wave number. Use your results from Part (a). Express your answer in terms of quantities given in Part (a).

###### FREE Expert Solution

(a)

The wavenumber, k = 2π/λ

Wavelength, λ = v/f

###### Problem Details

The de Broglie relation λ=h/p can be rewritten in terms of the wave number k as p=kℏ. Recall that wave number is defined by k=2π/λ.
(a) Using the fact that λ=v/f, find the wave numbers k1 and kcorresponding to frequencies f1 and f2. Express your answer as two expressions separated by a comma. Use f1, f2, v, and π.
(b) Find an expression for the uncertainty Δk=k1k2 in the wave number. Use your results from Part (a). Express your answer in terms of quantities given in Part (a).
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9431015849113464, "perplexity": 794.5877957236153}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107878662.15/warc/CC-MAIN-20201021235030-20201022025030-00320.warc.gz"}